I have read many fics where she becomes a doctor. Was this discussed in the show?
Off the top of my head (which is hit or miss) the only thing I remember that may have fueled doctor!Daph in fics was when Justin was with Ethan and he announced he was dropping out of school. He asked her what classes she was taking and she answered something like anatomy and biochemistry, which I assume one takes for pre-med?? I really don't know, but due to that and her stellar SAT scores, many writers make her a doctor.