I've personally dealt with this issue from when I was stationed at Ft. Benning. One thing is VERY important to remember:
Always keep a copy of the Georgia statute covering CCW for military service members on your person and in your vehicle along with your military ID (never travel without it!). Read it carefully and understand it...had a GBI agent tell me that I could carry concealed, but the firearm had to be unloaded at all times...and I don't recall if/what I found to dispute that.
The Columbus, Ga LEO's are complete jerks about this statute and WILL try to tell you it applies only to your duty firearm and only during the course of your duties in the military. This is a lie (they know it's not true) and should be addressed on-site with that statute....highlight the applicable section.
If you get any static from any Ga LEO when you politely and professionally provide the statute (don't EVER hand them your military ID, it's DOD property, they can see it from your hand), just write down their badge number, name, and demand that you speak to a supervisor in person immediately. Be courteous just once, if they persist, firmly remind the LEO to focus on the reason for the stop and that any continuing pursuit of the CCW issue will be deemed a violation of your civil rights as you have courteously provided the applicable statute.
Do not forget that once you cross the state line to leave Ga, the statute no longer applies. If you're a resident of a bordering town in Alabama, you can address the Alabama CCW issue for your being stationed neary-by. Our issue was that we lived in Alabama (Phenix City) and were stationed at Ft. Benning. We needed coverage in both states because of where we had just returned from. Easy to get worked out, you just have to be willing to do the leg work.