Is it permissible for this female student to travel by plane from Egypt to Saudi Arabia without a mahram, knowing that her maternal uncle will take her to the airport, her father will wait for her at Jeddah airport, and the journey takes an hour and a half?

A woman is not permitted to travel without a mahram, whether the travel is for an act of worship or for permissible reasons. The evidence for this is the Hadith of the Prophet (peace and blessings of Allah be upon him), and because travel often involves hardship and difficulty, and a woman needs someone to support her. More than one scholar has related the consensus of jurists on prohibiting a woman's travel without a mahram, except in specific, exceptional cases. As for a woman traveling for the obligatory Hajj without a mahram, the correct opinion among scholars is that it is not permissible.

In cases of necessity, if a mahram is unable to accompany the woman, especially when traveling by plane, there is no harm if a mahram escorts her to the airport and another mahram receives her at the destination, provided that the escorting mahram ensures she will be met by her mahrams at the other end.