She's cute! I've had Dobermans for ten years, they're wonderful dogs. I have a red boy now who's 8 years old, and the reds are awesome. He's the best dog, and he's adorable. His ears are cropped, I think it's more of a medium crop. It looks good on him, a long show crop wouldn't have framed his head very well. It wasn't my choice though, he's from the SPCA and his original family picked the crop. He was left in the lobby with no explaination of why, but his temperament is perfect and he's wonderful with kids and other pets.
Puppies shouldn't go home with their new owners until 8 weeks, though. In most states, it's actually illegal to send them home earlier than 8 weeks, and it would be a red flag for me if a breeder said I could take a puppy home earlier than that. You will have more work to do with socialization and training- those last two weeks that your girl missed with her mom and siblings are when they learn a lot of important lessons on behavior and how to act. Definitely enroll her in a puppy class once she's had her shots.
I really want a GSD for a second dog, but I have to wait a little while. But I will always have a Doberman. They're just amazing dogs.