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.
It is permissible for a woman to disclose her face, hands, arms, hair, and feet in front of her unmarriageable persons. A non-Muslim father is also a Mahram (unmarriageable person). He is also Mahram for traveling. So it is allowed for her to uncover the above mentioned parts before him and to travel with him, provided that she feels safe from all temptations in all cases.
Allah knows best.