You are looking for a summer rental or just to book on the fly? I know nothing about HH, but you might want to check some of the places out nearer to Savannah, like Tybee, or even further up this way toward Charleston like Seabrook, if you dig that "resort-y" lifestyle that HH sells.
VRBO might be worth looking into--I know a number of places listed there on our local fun beach communities allow pets.
“One day your life will flash before your eyes. Make sure it's worth watching.”
Gerard Arthur Way