Georgia does not issue non-resident permits.
MIL-DOT is correct. If you are NOT a Georgia resident, a Florida permit is honored. However, a Georgia resident MUST have a Georgia permit. Georgia does not honor out of state permits for Georgia residents.
Also note that it is very difficult to carry legally in the course of normal daily activities in Georgia--the list of statute restrictions on firearm possession is endless and includes places such as: anywhere alcohol is sold for consumption (restaurants), publicly owned or operated buildings (such as rest area bathrooms), and "public gatherings" (which are not well defined, but include sporting events, etc.), among others.
Also note that it is a FELONY to carry ON or even "a reasonable distance from any regularly scheduled stop" along the route of public transportation (ie. MARTA, any bus, train, aircraft)--this includes parking lots of the "terminal" as well!
Another poster once put it well: "Just about the only place you can carry in Georgia is walking up and down the sidewalk in front of your house, as long as it is not on the bus route."
You may keep a firearm in your vehicle without a permit, provided it is kept in the glove box, center console, or similar container--case law has defined that it must have a lid. It CANNOT be stashed under the seat. Additionally, it can be kept in "plain view" but that is also not well defined and is up to interpretation by the officer/judge. Note that open carry or any other on-body carry is not legal in Georgia without a permit.
As Cacique said, your best bet for Georgia carry is to get a Florida permit. However, consider that you won't realistically be able to carry many places outside of your hotel room or car, so IMHO it's not worth it just for Georgia. If you are interested in other states that Florida covers, go for it, but just the few places you will be able to carry in Georgia is not worth $117.