The thing is there are few fully organized data statistics. There other thing is that not all people breeding who are showing conformation are created equal. Some people will test their breeding dogs for 10 different things, and some will test their dogs for hips and call it a day. (And then again those same people who in the database only have a dog tested for hips, might at home have results for a vWD swab but the information isn't up in public. Or they know the dog can only be clear by parentage... but this is something that is 'invisible' by simply looking at databases) I wouldn't consider the latter ones ethical or responsible, but that doesn't stop their dogs from being in the show ring. Then there is the matter that not every dog produced by an ethical breeder being shown, is going to be owned and shown by that same breeder. Unless the dog is on a co-own, once that dog is sold, it's sold, the new owner makes the decisions. The new owner may or may not test the dog, regardless of intent of breeding.
One big problem I see as well with your project is that in order to find statistics or collect data you will be operating off assumptions, that simply cannot be drawn from statistics. You are going off the presumption that if a carrier animal is being bred to an affected animal, it is because conformation is being placed above health. But Dobermans have a lot of health issues, and from the people I've spoken to that are looking at health statistics rolling in from projects like the Doberman Diversity Project, and the VGL project, as well as pedigree research etc. the is an interesting trend - the dogs dying from DCM for example are often not dogs with an affected vWD genetic status (and furthermore just to confuse you, did you know that a genetically affected individual doesn't always translate to a clinically affected individual? And now there are reports that dogs who are genetically carrier, can be clinically affected also). So perhaps this affected animal bred to a carrier animal is paired together not for conformation reasons first and foremost, but rather because maybe they have unique longevity in their respective pedigrees. Maybe they are paired together because the pedigree would be the same or similar nick as a dog they produced in the past that lived to 13 years old, and happened to be a GCH, with excellent breed temperament. Unless you speak to every individual breeder, or create a survey for breeders to fill out explaining their reasoning for a particular mating, you may not get accurate statistics on that front.
Another example to look at - popular sire syndrome, this is a real phenomenon, but how do you tell which breeders went to that popular sire because he is known and produces winners, vs which breeders went to that popular sire because he is actually an excellent match for their bitch?
You are also neglecting ethical/reputable working line breeders. I have heard at least one say that while health is important to them, working ability is the most important consideration when matchmaking and producing dogs in their eyes. Is that not similar to someone who would prioritize conformation over health?
This is not to discourage you but rather illustrate some of the issues with your approach and the premise for your research project. It might be easier with some European countries where the breed club keeps health records and demand hard copies of the evidence rather than just relies on user-updates into a database, but then good luck getting the truth from some of the more tight-lipped protectionists, if you even manage to get in touch with someone from the breed club. The DPCA has refused to release studbook information in the past (though this was less about health research and more pedigree research of historical dogs). The DV is a nightmare to even get in touch with and if you do, good luck getting anything from them - as this is the same crew who declared after a 3 year study that DCM was not a problem in this breed. DobeQuest, as Mary Jo mentioned is not always reliable because it is often not up to date. My bitch's litter wasn't even added until this past December after a kind member here on DT added them to my request, and that did not include all the current titling and health info I have for her as well as one of her littermates even though they turned 4 in Feb. (The owner of the littermate and I agreed we'd just submit everything later in the year because we expect more results and additional titles by the end of Summer).
The other thing is, because several of the diseases in Dobermans haven't been narrowed down genetically, we do not know with certainty which nick might produce what. Someone could be making a nick based on pedigree research that they think is safe, or will hopefully increase longevity, but then when the pups hit the ground they grow into 10 different issues they'd never seen before. Biologists agree genetic diversity is important, and there seems to be correspondence between lower COI and longevity... but there isn't even one test out there that fully evaluates all aspect of genetic diversity. It depends whether you believe more in a system based on hetero/homozygousity (such as Embark) or rare/common alleles (VGL/BetterBred). We know the breed's average longevity is decreasing, but is it really because breeders are choosing conformation over health? Or is it because previous breeders painted us into a corner we didn't see coming and now we are suffering the consequences in spite of our best attempts to fix it? We can debate this until the cows come home, but my point is that you cannot draw conclusion about a breeder's intent and a breeder's reasoning. Which makes the basis of your project (putting aesthetics over health) difficult to prove. Furthermore I'd argue that there is a difference between aesthetics and structure, and both elements contribute to a dog's conformation. You can have a dog that is beautifully structured, well-balanced and harmonious looking - this is structure, this is in terms of the dog's biomechanics and functionality, according to breed standard and would contribute to soundness (health). But then, that same dog might not be super typey even if they objectively fit the standard and have decent/correct type, they might be a more moderate sort, this is more aesthetic.
Do some breeders breed to win? Sure. Do some breeders make breeding decisions based on aesthetics over structure? Probably. Do some breeders put those things above health? I don't doubt it. Are there breeders that produce dogs with the fashions and trends of the day, and what is currently winning even if it might technically be incorrect or not called for by the standard (if not opposite)? Yes. But there are also breeders who breed dogs with their ideal in mind according to their interpretation of the standard, and their priorities towards health. There are breeders who focus on structure in the long run and tweak aesthetics as they go, regardless of whether they are producing top 20 dogs or not. You have breeders producing top 20 dogs almost as an aside of what their main goals are in their program, I'm sure you could draw a Wien diagram even of dogs produced with top 20 as a goal, dogs making it into the top 20 vs dogs not produced with top 20 as a goal but who ended up there for xyz reason. My question is how do you distinguish all these categories from one another? (And in Europe you can substitute top 20 for world champs, specialty champs etc.)
I think as others have suggested you are best first narrowing your scope. Decide what you want to focus on. Pick one thing then from that one thing you'll be able to find the right resources to help you. And consider that you will probably have to survey rather than just gathering statistics based on data such as OFA health tests. But I'd be careful in the way that you survey, because the show and work Doberman community is very small in North America. A little bigger in Europe but then depending on where in Europe you are looking at, you also have to factor in socio-economical contexts. The accessibility to a holter monitor device is not going to be the same in Albania as it is in Massachusetts, both financially and just in terms of locating a device, and I do not think it would be fair to automatically dismiss breeders from poorer countries as being somehow less responsible if they are trying to make thoughtful breeding decisions.
I can think of one breeder in a Balkan country who once lost a dog due to incompetence from veterinary professionals (at multiple levels) so he went and got his own veterinary license to try and better care for his dogs, but that doesn't mean he has access to all the equipment and devices that he would in the West.
So there are a lot of factors you will need to filter in order to gather data as objectively as possible.
In addition to the links provided above, I would recommend finding the Doberman Diversity Project on facebook to see if you can access more information and data, I would also recommend checking out http://dobermanngenealogy.dk/
You will need to write to the admin to be able to sign up, it might be easier joining her on Facebook. Someone tried to sabotage this database but it is possibly the largest in the world (we are talking 400 000+ dogs, including dogs tracing back to Mr Dobermann's dogs) the owner keeps death and health statistics as objective and truthful as possible, she will not write 'suspected cardio' or 'cardio' if it is not confirmed.