She's still fairly young, so you've got a good chance they will--you may have to post a little longer than is typical. That depends on the shape of her crop, but usually a dog will need to be posted at least until they have finished teething--so until they are 6 months old. But many dogs may need to be posted longer; it depends on the individual dog.
It sounds like you posted them and just left them in that bandaging? You should only leave ears posted for 3 or 4 days at a time, take them down, clean them out, let them air dry for 30 minutes or so (maximum) and then post them back up again. If they get wet or unusually dirty, if the post pops out of the bottom of the ear, or if they get smelly like your pup's did, you should take them down right away, clean them up and evaluate them for signs of infection or irritation before you put them back up again.
You are correct that they should not be posted if there are any scabs, raw areas or irritated skin that tape or the post will go across. Did she have to get antibiotics to deal with an infection?
There are a few tutorials here on posting with step-by-step pictures which should help you out.
One about posting--this is the method a lot of us use; we recommend it as being the easiest method that will give you good results.: https://www.dobermantalk.com/ear-cro...acker-rod.html
This method is pretty much the same, except it leaves out the zip ties and the double sided tape when you are preparing the post. With show cropped ears, which are very long, zip ties help, but they aren't necessarily needed, depending on the dog's crop. DON'T
use vet wrap, however. It is very easy to get it too tight if you're not used to using it, and it tends to shrink if it gets wet, so it can really harm your dog's ears by cutting off the circulation to the ear tips. The tips may even die because of lack of blood flow. Tape her ears at the bottom, the middle and the tip (the post should be longer than her ears are, and you should tape the entire tip to the post) to make them secure instead. https://www.dobermantalk.com/ear-cro...my-method.html
Here's another about removing the posts gently: https://www.dobermantalk.com/ear-cro...ear-posts.html
If you can post pictures of her head and crop, both from the side and the front, we should be able to tell you a little more about how to handle her ears. And if you tell us about where you live, there may be a dobe member nearby you can contact to get some in person help. A little hands-on help can go a lot further than an explanation over the internet.
We need to see pictures of your puppy anyway. We Love Dobe pictures here!!
Welcome to DT from Colorado!!