I would think, even with that draft, you could do most of the ICW down to Charlestown, SC. You probably could not navigate through those Georgia swamps at all and should consider heading offshore at Charleston, then you can duck back into the ICW at Fernandina Beach, FL. Keep in mind that you'll have lots and lots of bridges to contend with, but overall the depths appear to be more than adequate.
Now, if you have a crew, and the weather cooperates, the coastal passage would be very doable all the way to Key West. Like others have suggested, I would consult the Cruisers Net for the most up to date information. Additionally, I would wait until at least October 1 before making the trip.