We're locals so my son went to the parks a lot as an infant, and endured the Florida heat pretty well.
The baby care centers are fantastic, and for more than just nursing. They're usually quiet with few people in there, they're air conditioned, they have clean places to change a diaper. I would use them every single time we went to the parks.
Make sure you stay hydrated, drink way more water than you think would be necessary to keep your milk supply up. I was amazed at how being just a little dehydrated really took a toll on my milk.
I always got too hot wearing my son in the parks during the summer, he and I were both happier with him in a stroller where he could lay flat and kick his legs. We have a sun umbrella and a portable fan that clips to the side of the stroller, and he never seemed to get too hot.
Be prepared to be flexible! Your daughter might completely change her schedule/sleep patterns/feeding patterns, and its easier to roll with it than trying to force her to stay on a schedule, you can do that when you get home. Take plenty of breaks and have fun!