If you are active military - you can carry in GA without a permt or GFL. Infact you can carry in more places than someone with a GFL. But you hav to be on "active" duty for this to apply.
You do not have to be active military for this to apply, you just have to be in the military service of the state or the United States. It is true that you can carry in more places than people just with a GFL. Just show your military ID.
There is an attorney general's opinion where the question was asked can active duty carry without a GFL and the answer was yes. They only answered the question that was asked without much elaboration. This has been misconstrued by people that think you have to be active duty for this to apply. Read the law yourself. It is 16-11-130.
Here's a link: