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.
The majority of scholars agreed in opinion that the child is considered a Muslim if one of his/her parents is a Muslim. Since the father of this woman is a Muslim then she is also considered as a Muslim. Nonetheless, when she reaches the age of puberty, if she refuses to embrace Islam, then she is an apostate and therefore it is not permissible for a Muslim to marry her.
However, if we suppose that she is a Muslim, it is not permissible to marry her except with the permission of her guardian as the Prophet said: "A woman cannot get married except with the permission of her guardian." [Abu Daawood] If she fears that her father will prevent her from getting married without a sound religious reason, it is permissible for her to take the matter to the Muslim community to remove the harm she is undergoing.
To conclude, it should be noted that it is an obligation to advise this girl and remind her that her fate in this world and in the Hereafter depends on her becoming a Muslim. Besides, it is not permissible for her to obey anyone about this matter whether it is her mother or anyone else.
Allaah knows best.