Most states that honour the CWP of another state do so on the condition that permit is a RESIDENT permit. If you move from Georgia, you will no longer be a Georgian... thus your new state might not recognise your Georgia permit.
You should definitely get a new resident permit in the new state in which you will be residing. Not only to assure you are safe and legal in your new state, but in the event you travel to any OTHER state.... nealry every state that does recognise out of state permits does so on the condition they are RESIDENT permits. Thus, if you no longer reside in Georgia, and are travelling in Kentucky with some other state's driving license and number plates on your car, your permit will NOT be recognised in Kentucky which only honours RESIDENT permits from other states. Your Georgia permit will no longer be your RESIDENT permit.
Get it right, the risks of getting into knee deep shark-infested water is too great... who knows, you could end up being charged with a felony for carrying concealed without a proper permit in some other state..... no more guns for you, and not much money, as most of what you have will get swallowed up in the endless whirlpool of courts and lawyers.
Before you leave Kaintuck, see what might be done to promote their laws getting changed to actually issue non-resident permits... and if it costs your Georgia resident permit to move, oh well... find out if you can carry open in Georgia (I rather think you can....) the trouble with moving is, you are MOVING.... shifting residence to another state.