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 have already clarified and still repeat that residing in a non-Muslim country has many disadvantages, it is for this reason that it is not permissible to travel there except for a necessity or a dire need whether this is for the purpose of study or else; for more benefit, please refer to Fataawa 86405 and 90561.
This is even more confirmed in regard to a woman especially if she will travel without a Mahram and her father objects her doing so.
Therefore, if the above circumstances apply to you, then it is not permissible for you to travel there. It might be that if you fear Allaah, Allaah will make a way out to your difficulties and facilitate your affairs.
Hence, we advise you to seek to study medicine in your country, and if medicine is not made easy for you there, then you should study other specialties that suit a woman. The benefit of preserving your religion comes in priority over all other benefits.
However, if there is a real need for you to study medicine in that country, and you are accompanied by a Mahram during your travel, and you are safe about your religion by residing there, and your father does not have a religious sound reason for refusing, then it becomes permissible for you to travel. However, if this travel may cause you some problems with your father, then you should not travel.
Allaah Knows best.