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.
Accepting the person who proposes for marriage is the right of the woman/girl whom the man had proposed to; it is for this reason that the Prophet put the matter in her hands as per the Hadeeth of Ibn ‘Abbaas in which the Prophet said: “A woman who has been previously married is more entitled to her person than her guardian [i.e. she should not be given in marriage except after consulting her]; and a virgin woman should not be given in marriage except after her permission, and her permission is her silence.” [Muslim]
Therefore, in proposing for marriage, the consent or presence of the guardian is not a condition, but his consent and presence are a condition only when concluding marriage. Moreover, the guardian must be a male; and a woman is not permitted to give herself in marriage, nor is it permissible for a woman to give another woman in marriage. For more benefit on the order of the guardians of a woman, please refer to Fataawa 83338 and 86555.
Also, it is a condition that the guardian be a Muslim, and it is not permissible for a non-Muslim man to give a Muslim woman in marriage even if she is his daughter. Therefore, if a woman has no Muslim guardian, then it is the Islamic judge who marries her off, and if again there is no Islamic judge, then she should entrust a just and trustworthy Muslim man to marry her off as clarified in Fatwa 88488.
Allaah Knows best.