The father and I were never married but, he is on the birth certificate. He has been ordered to pay child support. He has a un stable living environment. He lives with his girlfriends parents, has no dependable vehicle, just recently started seeing our daughter after not seeing her for over a year. I have not denined him visitation. But, I feel that his life is very unstable to have our daughter in. I'm wanting full custody

Unless she lives with him part time, you do have de-facto full custody. From what you are describing, your issue is visitation, which having fill custody would not eliminate. If you truly believe that he is not stable, you need to go to you LOCAL court and ask the clerk's office what the procedure is in your locality. Once custody/visitation are awarded, you then need to express why you believe that his visitation should be limited or supervised. Courts very rarely strip parents of visitation rights and it will not happen in this case unless you can prove that he is a continuing danger to the child.