That is really a shame she was taken from her littermates so early. To compensate you are going to have to socialize her even more so.
It is not too early to start potty training your baby puppy but don't have huge expectations. Her bladder is very small and she just can't hold it long, it is just a fact of young puppies, so she will be in housetraining for quite awhile. But you can help the training go easier by training her early.
Take her outside often so she begins to associate the grass with potty time. The more times she goes out there, the easier it will be for you later. Several times per hour take puppy outside. Take her outside after she wakes up - even if it is a very short nap. Take her outside first thing in the morning - before you eat or do anything take care of her. Take her outside right after she eats her meals or drinks a big drink. Take her outside after a play session. Take her outside when you see her sniffing...(you get the idea). You will learn and get a feel for what sniffs mean I need to go out. You have to keep a close eye on her and don't let her go off and learn to poop and pee in secret. When you cannot watch her place her in a safe place, a small crate. A crate will help her stay safe and will help her along in her potty training.
She should be able to move around but the crate shouldn't be too big or she will use one side to use the bathroom, which defeats the purpose. Don't leave her in the crate for more than an hour.
When you take puppy outside, repeat the words "go potty" over and over until she goes. When she goes praise her a lot and you can even give her a treat and play with her. Going to the bathroom outside becomes a very positive thing. Soon when you take her outside and say go potty her reaction will become to use the bathroom outside. Doberman puppies are VERY smart, she will catch on fast.
When you find accidents inside DO NOT punish her. Those are your fault. She can't hold it yet and needed to go really bad. It is your job to take her outside. Don't get mad at her. There is no reason to get mad and it is useless.
If she goes to the bathroom in front of you simply say a firm no, scoop her up, and let her finish outside. When she goes outside remember to praise her a lot and maybe feed her a treat. I also like playing with them afterwards, a fun game with their people is also very motivating, as much so as food for some Dobes.
But expect accidents b/c she won't be able to help them for awhile.
As she grows up, her housetraining will get much easier as she gains more control of her bladder.
As far as the crybaby thing goes, what do you expect? She is a young puppy and was taken too soon away from her littermates. She is going to cry.
Crate training is just that, training. If you know you have given her lots of attention and she has peed and pooped yet is still crying in the crate, let her cry. Don't let her win. She is a puppy and it is natural for her to whine when left alone in a crate.
But don't give in, NEVER EVER go to her and let her out when she is crying. Once again, Doberman puppies are very smart and she will learn crying gets her a reward. She gets to get out when she cries. You don't want her making that association; they learn quickly what works and what doesn't. Just ignore the cries and do not yell at her or get mad. Wait it out, it will get better.
Only let her out when she is quiet. Be sure to put some safe toys inside the crate with her too, so she isn't totally bored.
To crate train my puppies I toss a treat (or two) inside the crate and say "kennel up", when the puppy goes inside they get rewarded. I do this lots, sometimes I close the door, sometimes I don't. Sometimes they stay in for a bit, more often than not they don't and I let them out. They get a treat for being quiet and learn what behaviors get rewards and what behaviors get ignored quickly. Also don't use the crate for punishment and don't keep them in there for hours, they are babies and can't be expected to hold it for that long.
Good luck.
