We lived in Jacksonville (FL) when I was pregnant with my youngest and we went several times when I was pregnant, the last being when I was about 6 and half months along. There are tons of benches everywhere, so sit frequently, drink lots of water, cut through air conditioned buildings (most of the shops and things have a front and back entrance so you can just walk straight through) if you are going during the summer, take it nice and slow. If you need a place to sit quietly for a while in airconditioning I would recommend the baby care centers (there's one in each park). And avoid the rides that they tell you to. I remember wanting to do the safari ride in Animal Kingdom and suddenly noticing that there was a pregnant women should not ride and thinking "oh come on it's not a rough ride" but being good and staying off it. When I rode it post pregnancy I was surprised at how many jerks and rough corners there were. Disney knows their rides, so follow their warnings and you should be fine.
Enjoy your trip!