Congratulations. It is incredibly humid and hot in September so your baby is likely to be extremely fractious and tired. He/she will need to be kept very cool and well hydrated which will mean visiting the parks early in the morning and probably leaving after a couple of hours or so.
If you're staying on-site this won't be too much of a problem as you can dip in and out. It will be a bit more difficult if you're off site. Personally, I think there would be better times to visit, November, May etc not because of the baby's age but because of the conditions. However, with careful planning and LOTS of breaks I suppose it could work...but be prepared for a cranky baby!
Good luck!