Legal Question in Family Law in Georgia

You don't say who you are or how you got custody. Absent consent by one or both parents, or the approval of the state, no one can adopt a child.

Although a non-legitimated father has no custody rights, the law requires that he be served (or consent) to an adoption. His potential rights can be terminated for failure to support or see the child (usually for at least 1 year, so you may be premature asking about a 7 month old). His failure to legitimate can be a factor, but he can very possibly defeat an adoption by filing a legitimization and paying support.

Adoptions are impossible without an attorney and as a general rule terminations are done during the adoption process. If you are seeking to adopt, meet with an adoption attorney. Nothing in your post gives any information that qualifies you to adopt, and merely having custody is not always a precursor to adoption. It is extremely difficult to terminate a mother, and unless you have the state's cooperation (such as a DFCS case) that is probably not likely as to a 7 month old. Note that where DFCS gets involved, people on their adoption list have priority over most other people.