My first question would be, where are you staying? If you are staying at a monorail resort, such as the Poly, or especially the Contemporary, its a no brainer to just go back to the hotel. August in in Florida is going to be massively hot. While my youngsters at that age easily napped in their strollers, it was usually not in 95+ degree heat and humidity. They also would normally nap with a blanket or something covering them, both to keep the sun out of their eyes, and to help them not be distracted by everything going on around them...an option not available in the Florida heat.
At that age, you are probably hoping for at least a 30min nap, with 60min being a vacation gold standard nap. Taking into account the time you are going to take trying to find a spot that makes a nap even possible, without the noise, sun, heat of the mid day, then putting the baby down and hoping they actually fall asleep, you are probably looking at 60-90min period of time. If you are anywhere on property, I just go back to the hotel, let them get a good nap in, which will hopefully make your afternoon-evening at the park longer and more enjoyable. A couple hour break in the AC at the hotel won't hurt the adults in the group either.