The Lowcountry and Georgia coast are very kid-friendly, with the possible exception of some B&Bs that are clearly not designed for younger children. If you have any doubts about this, feel free to inquire. Otherwise, there are no special precautions unique to this area.
There are no zoos per se in the area, but animal-lovers of all ages will enjoy Charles Towne Landing  in Charleston and Oatland Island Wildlife Center  in Savannah. Better still, take the kids on nature outings to the amazing National Wildlife Refuges in the area.