Listen to me, you might have to get an attorney. You NEED to fight to keep jurisdiction in FL. How long has she lived in GA for? In order to be a resident, it's usually 6 months to a year before she can actually file for anything, legally. A lawyer could squash that easily. Also, child support is VERY high in GA as compared to other States., even higher than FL.
I was you 5 years ago. Please try to realize that the problems now won't go away, sometimes they get worse, much worse. You have to be a very strong person to deal with all of the crap that exes can bring on.