Is our planning to marry without her family's consent compatible with Islamic Sharia, and if permissible, who can be the woman's guardian (wali)?

The disbelieving relatives of a woman have no guardianship over her after she embraces Islam. If there is a Muslim ruler in her country, he is her guardian, according to the Prophet’s (peace be upon him) saying: "There is no marriage except with a guardian, and the ruler is the guardian of whoever has no guardian." If there is no Muslim ruler, then the reference point for Muslims in that area, such as the director of the Islamic center or its imam, shall undertake her marriage contract.