I know Alabama recognizes Georgia's permit as I checked a few weeks ago before barber motorsports vintage bike race weekend but I'm not sure if Georgia recognizes Alabama's I don't see why not. But Check up on that on your own though.
google shows this:
Georgia does require you have a permit to cc or oc so according to that you should be covered for either. Georgia also allows you to OPEN carry in your vehicle without a permit.
Enjoy the show!