All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
A woman who believes in Allah and his Messenger does not have any right to travel without being accompanied by a Mahram (unmarriageable man). The Prophet said: “No woman who believes in Allah and the last day should travel a distance of a day and night journey unless her Mahram is with her.”
Ibn ‘Abbas narrated that the Prophet said: “No man should stay with a lady in seclusion except in the presence of a Mahram.” A man stood up and said, “O Allah's Messenger! My wife has gone out intending to perform Hajj and I have been enrolled (in the army) for such-and-such campaign.” The Prophet said, “Return and perform Hajj with your wife.” [Al-Bukhari and Muslim]
All the scholars of Islam agree that a woman should not travel anywhere without a Mahram. Some of them permitted her to travel for performing obligatory Hajj only accompanied by a trustworthy group of women. They did not even allow her to travel for supererogatory Hajj. Then how would she be allowed to travel to another country for studying, which is not compulsory on her. Islam always protects the religion, soul, mind, honor and wealth. A Muslim should give priority to preserving these things before daring to perform some supererogatory work.
Allah knows best.