I am not a Georgia attorney, therefore I cannot give you advice as to Georgia law. However, I am an attorney with experience in Federal Crimes.
A Misdemeanor Crime of Domestic Violence is defined in 18 U.S.C. 921(33) (A) . . .the term “misdemeanor crime of domestic violence” means an offense that–
(i) is a misdemeanor under Federal, State, or Tribal  law; and
(ii) has, as an element, the use or attempted use of physical force, or the threatened use of a deadly weapon, committed by a current or former spouse, parent, or guardian of the victim, by a person with whom the victim shares a child in common, by a person who is cohabiting with or has cohabited with the victim as a spouse, parent, or guardian, or by a person similarly situated to a spouse, parent, or guardian of the victim.
You need to look at the Georgia law, for your simple battery, to see if one of the ELEMENTS of the crime is a battery which is DOMESTIC in nature (spouse, parent, etc....) Not only does the crime itself have to be against one of these people, but the law itself has to be about domestic violence.
Look to see if the statute makes it a crime to commit a battery against a spouse, parent, etc.... If it is just a battery (i.e. crime to commit against anyone), then you are probably not in violation of the Federal restriction.
As an update to the answer to this question, earlier this year, the Supreme Court of the United States, in United States v. Hayes, decided that a "misdemeanor crime of domestic violence" includes any misdemeanor offense in which there exists the use or attempted use of physical force, OR the threatened use of a deadly weapon, AND such act was committed by a person with a specified domestic relationship to the victim, regardless of whether the offense was charged under a specific domestic violence statute. So, (1) your prior conviction will be identified as one of "domestic violence" if it was charged under GA's Family Violence Act (but under federal law that is irrelevant); (2) you are allowed to petition the State of Georgia to reinstate your right to possess a firearm under STATE law after 5 years, but that has no bearing on federal law (18 USC 922); (3) you will have to either have the conviction vacated, or obtain a pardon from the Georgia Department of Pardons and Paroles; and (4) if your rights are restored (see #3), such will be indicated in the National Crime Information Center (NCIC) database.