If the father takes her keys she can still walk out, get a cab, call a friend etc. However, she probably won't be allowed to return to live in her father's house if he feels so strongly about her leaving. If he's drugging her at night obviously that is against the law and if nobody wants to get the police involved and you're ready to support her full time then she should move in with you now. However, keep in mind that she obviously loves her father and by leaving she will be cutting ties with him to be with you which could cause major problems of resentment and wonder later on down the line.
I thing the logical thing would be to go to a family councilor now to resolve any issue and hopefully build some sort or relationship with you and her father, even if it is just cordial. Get the entire family involved in the counseling if at all possible, it's never a bad idea to just talk and more

