I believe what's posted above to be out of date (2010). And, I'd question any F&G law seven years old. Personally, I'd call the F&G or look for an on-line update.
Let me add....
On other pages of the Georgia code, it does talk about youth hunting, and the term AIR RIFLE appears, and with no restriction as to caliber. And, if you read the code correctly, the .22 caliber or smaller rimfire, (note the comma), air rifles...
I sure as heck call the local office after rereading the material.