You need to file for custody and child support. There may be an agency in Virginia which will help you with collecting child support. When you file in court, he can always counter-sue for custody or visitation. That doesn't mean he has grounds (Since he has had no contact, it appears that he doesn't) but he can ask.
You should be aware that the Georgia courts, not the Virginia courts, may currently have exclusive jurisdiction to award custody (See the
UCCJEA). Virginia will have jurisdiction only when the child has lived there for the greater part of her life (Thus, you took her to Virginia four months after she was born, Virginia jurisdiction would start right about now; if you took her there earlier, jurisdiction would similarly be in Virginia).