It's a little tough with a small child because you don't want to get them sick. If it's not a concern take advantage of the lighter crowds and the cooler weather.
MGM has a lot of indoor or covered activities. Most of them are good for small kids too. Beauty and the Beast show, Little Mermaid Show, Bear in the Big Blue House, Great Movie Ride, and Indiana Jones are all covered. They also take a while to get through so you will be covered fro about 20 - 30 minutes on each.