What are the father’s rights if he isn't on the Birth Certificate?

My child was born out of wedlock in April 2010. Her father wanted nothing to do with her and kept denying her so I got a DNA test done, results came back positive. He has seen her three times in January 2011. His name wasn't put on the birth certificate and she kept my last name. As time has passed, he's not done anything as far as ask about her, never contacted me, never supported her in any way. Within the last year he's managed to have a child by and marry someone else. Now all of a sudden this past May he's decided that he wants to be dad of the year so to speak. I’ve let my daughter spend the night a few nights with him so they could spend time together. Now he wants to take me to court for joint custody of my kid. She is stuck to my hip so it makes it that much harder. I've been with my fiancé since March 2010. We are due to get married in November. My fiancé is in the navy, so I would move to where he is getting based, plus he has raised my kid since she was born. What are my rights? Can I move out of state with my child? Do I need to let him take me to court before I let my child go back with him? It's a mess but any help/resources are greatly appreciated!! Feel free to email with stuff that can prepare me with this matter.