My daughter was called a nurse when she started playing with a stethoscope. Innocently said, but tell me this: if she had been a boy, would she have been called a doctor?

I would've called her a doctor, too! People in general have different perspective in life. Whoever addressed her as a nurse could possibly, at some point in his/her life, wanted to become a nurse himself/herself. I suggest not to bank on on the idea of stereotypes with this situation. Because in the end, a nurse and a doctor are both decent, rightful and promising professions and vocations.