You never had a chance in the matter. Sorry.
Something sounds fishy......
Either with this question or with the girlfriends father. OR...... I have ALWAYS told my kids that I will be more then happy to be their "bad guy" or their scapegoat if they ever needed an excuse to get out of doing something they didn't want to (such as go over to a friends house.) Maybe she does not really want to move in with you or maybe she is not really ready to leave the shelter of her father's house yet. There are too many variables here........
Well if you are in the US and your girlfriend is 20, it is her that is not moving in with you. Hear father can't stop her. She has weighed her options and made her decision.
If you both are 20 then I do not understand why her father is being stubborn. If she really wants to move out then her dad should not stop her from something she wants to do. Though, I can understand if her father is just worried about her, but other than that if you both agree on moving out then he shouldn't stop you or her.