In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If your daughter has a good intention behind her desire to learn medicine and practice it, she will receive a great reward. So, she needs to confidently anticipate Allah’s Reward, have a sincere intention, and carry on with her studies.
Answering your question, The Permanent Committee for Scholarly Research and Ifta’ in Saudi Arabia, states:
Learning medicine is a collective obligation on Muslim men and women as they are both needed to provide medical treatment for men and women. If women go out of their homes dressed immodestly or semi-naked, in violation of the Islamic dress code, or making a public display of their adornment or charms, this is prohibited.
However, if your daughter is as you described and she wears Islamic clothing that covers all her body, does not reveal what is underneath it, or show the shape of her body, then there is no problem in her going out for a necessity.
In fact, she should continue studying in the Faculty of Medicine, and specialize in branches related to women and children. The Ummah (nation based on one creed) is in need of Muslim women doctors, so women will not be compelled to undergo examination by male doctors who will see their awrah (private parts of the body that must be covered in public) when delivering their babies or diagnosing their illnesses.
If this student has a good intention behind her desire to learn this profession and practice it, she will receive a great reward. So, she needs to confidently anticipate Allah’s Reward, have a sincere intention, and carry on with her studies. May Allah grant her success and guidance to the most righteous path!
Almighty Allah knows best.