Quoting LoBrew:" How difficult would it be for me to get the courts to approve of me moving to a different state?"
You would probably need to show reasons your life would be better there- better job, better living conditions, if you move somewhere with supportive family around that is always a bonus. SO and I have looked into this for financial reasons and he would basically have to leave and get a solid job, housing etc so i can provide the courts with my request and have the proof that we are better off leaving. But I have 50/50 custody so it might be easier for you, since he hasnt even seen her. If anything, you may have to agree to travel with her for his visits which would actually make it much easier for you to monitor his interactions with her- but that might not even happen. He could prove himself to be unfit and you could do whatever you wanted.
Like if we left, I would most likely pay 100% of the travel costs for LO to see her father.