I agree with Lina, very sensible advice. I didnt feel able to respond with much advice, having not been in a situation like yours, but my feeling is that if you move, after you get a routine sorted with regular visits, stick to it religiously. That way your daughter can adjust to the new situation and soon get to know when she will spend time with you. Kids love things to be predictable, it makes them feel secure.
Far from hurting your daughter, you seem like a conscientious caring Dad who will always do the best for her, I wish you all the best, and I'm sure your little girl will always be sure of her Dads love.
I agree, do this while she's young but mostly wanted to say there is a HUGE difference between getting on with your life and abandoning your child, though it sounds like the mother may see it as an opportunity to play more games.
There is also no reason why you shouldn't go for full custody is mums not capable of caring for her properly herself.