My boyfriend has been providing for my child and we may move out of state. Can my child’s father prevent me from moving if I have full custody?

I’ve been living with my boyfriend for almost a year now. He has been providing for my daughter and I. But his job may have him moving to a different state. I’d like for us to move with him, but I’m worried that my child’s father will try to prevent that. He and I were never married. His name is on her birth certificate though. If I were to move I have absolutely no problems with making sure he can see her and be able to visit and spend time with her. What I want to know is if he can prevent me from moving?