is it legal to leave the state with my daughter, without her father, because he is abusive to me?

Do you have a court order that gives him timesharing/visitation rights?  If so, then you must get a court order or a written agreement from him letting you move with the child.  If you don;t have a court order yet, you could move, but he could file for an order making you return with the child and an injunction prohibiting you from taking her out of the state again.  Either way, if you want to move, the best plan is to get a written agreement from him or a court order letting you go.