Praise be to Allah.
Hajj is only obligatory for the one who is able to do it, because Allaah says (interpretation of the meaning):
“And Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind owes to Allaah, those who can afford the expenses (for one’s conveyance, provision and residence)”
[Aal ‘Imraan 3:97]
Being able to do Hajj in the case of a woman includes having a mahram who can travel with her and having enough money for herself and her mahram, because the expenses of the mahram’s Hajj are to be paid by her, because he is only travelling for her sake.
If a woman does not have a mahram who can travel with her, or she does not have enough money for that, then Hajj is not obligatory for her.
If Hajj is not obligatory for her, then she is not sinning or falling short by not doing it, and in this case she does not have to delegate someone to perform Hajj and ‘umrah on her behalf, rather she should wait until Allaah enriches her and makes a mahram available for her, then she can do Hajj for herself.
The father has no right to prevent his daughter or his son from doing the obligatory Hajj.
If she is physically and financially able to do Hajj, and she has a mahram who can travel with her, then she should ask her father for permission. If he does not give her permission then she should go without his permission, because there is no obedience to any created being if it involves disobedience towards the Creator.
The fact that her father will not let her does not make it permissible for her to delegate someone else to do Hajj on her behalf.
This impediment may be removed, and al-Haafiz Ibn Hajar said in Fath al-Baari (4/70) that the scholars are unanimously agreed that the one who is being detained (in prison and the like) should not delegate someone to perform the obligatory Hajj on his behalf, because there is the hope that he will be released.
This has been discussed in the answer to question no. 41950.