All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Children are not permitted to obey their parents in abandoning seeking knowledge that is obligatory on every individual even by travelling abroad, if there are people who would carry out these obligations, and there is a Mahram (non-marriageable relative) who would accompany the girl in her travel. However, obeying the parents comes in priority over seeking the knowledge that is an obligation on the community (i.e. if any member attained it then it suffices the entire community).
Indeed we thank you for your interest and zeal in studying the Quran and the Prophetic narrations, and we advise you to be frank with your parents and speak to them in a wise and good manner explaining to them that you wish to study the Islamic legislation and that you are reluctant to study medicine. However, if they insist on you to study medicine then you should put in priority their wish over yours, and you can, along with studying medicine, study the Quran and the Prophetic narrations by reading books, listening to tapes and asking scholars about any matter that you do not understand. By doing so, you would have indeed achieved both goals: pleasing [and being dutiful to] your parents and learning religious knowledge according to the extent that Allaah makes it easy for you.
Allaah Knows best.