The father of my son has not been there for our baby... he didn't sign the birth certificate and hasnet paid child support, he even changed his cell number so its pretty clear to me he doesn't want anything to do with his son, his family does not call either... my son is now 6 months. Is it possible for full custody to be allowed to me after my son is 1?

First, have you gone to court for support? Has he been declared the legal father?

If you were not married, then you have full custody by default. You don't need to do anything unless he goes to court.