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.
This woman must take the initiative to embrace Islam regardless of whether or not her father agrees; Allah Says (what means): {And We have enjoined upon man goodness to parents. But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them. To Me is your return, and I will inform you about what you used to do.} [Quran 29:8]
Moreover, the Prophet said: "There is no obedience if it entails disobedience to Allah; obedience is only in what is permissible." [Al-Bukhaari and Muslim]
The guardian of a woman should be from the people of her religion. Therefore, if this woman embraces Islam and her father remains as a disbeliever, then he has no right in marrying her off. The difference of religion prevents one from being a guardian who marries off a woman. Allah Says (what means): {…and never will Allah give the disbelievers over the believers a way [to overcome them].} [Quran 4:141]
If she has any Muslim guardian, like her brother, then her brother marries her off. Otherwise, it is the Muslim judge –or whoever acts on his behalf –who marries her off. If there are none of the above, then she gives permission to a just and trustworthy Muslim man to marry her off.
Ibn Qudaamah said:
"If a Muslim woman has no guardian and there is no Muslim ruler, then there is evidence which proves that Imaam Ahmad is of the opinion that a just and trustworthy Muslim man may marry her off with her permission." [End of quote]
For more benefit, please refer to Fataawa 123472 and 131340.
Allah knows best.