September and October are probably the best times to go. Less crowds and not too hot. We always go around that time and have a great time!
I love going in Sept because of the low crowds and the free dining promo, but in my opinion Sept can be and usually is very hot and humid. Also the peak of hurricane season. October tends to give more of a break in the weather I think.
I've also gone the week after Thanksgiving/first week of Dec. Very low crowds, nice holiday decorations. But, you run the risk of catching a cold snap. When we were there we didn't particularly feel like getting in the pool because it was a bit on the cool side and we didn't want to make the walk back to the room being wet. Also, a little more expensive that Sept.
We flew with our son at age 1 & 2 for a 2 hour flight. At one year old, bring snacks/bottle/sippy cup especially for take off and landing. The eating and swallowing is usually comforting and helps equalize the pressure in their ears. Check the TSA website for restrictions on what food / drink you can bring through security. Our son was on formula at the time and we had a few bottles of water with us so we could mix up the powder as needed. TSA website said you could bring milk, juice, formula...for an infant, but apparently you could NOT bring the water to prepare the powdered formula. They actually told us to mix up a bottle of formula using the water we had and then it was ok to bring the bottle through, but we had to throw away the extra water....very frustrating experience for first time flying with our son. Also, I think they have a thing against ice....
If you happened to be able to get a flight around a normal nap time, you might get lucky have your daughter sleep some of the way down. We found that traveling with a 1 year old was easier than a 2 year old. At 1 he didn't really understand what we going on, and just sort of went along for the ride. At 2, he realized we was strapped into a strange seat for take off and landing an freaked out.... Have you decided if you are going to fly as a lap baby or with her own seat? Something to think about.... people have very strong feels on both sides of this issue.
Agree with other post about bringing something to help easily identify your stroller in a crowd of strollers. Because it is a matter of when, not if your stroller gets moved - usually by a CM organizing or mananging a stroller area. We put a bright green luggage tag on our stroller handle.
If you can keep your "normal" schedule as far a napping and bedtime, you greatly reduce you risk of a complete melt down. Our son always took his regular nap(s). We are lucky though, he'll sleep in his stroller. Around nap time, we'd usually pull into a counter service restaurant that was air conditioned and relatively quiet, have a drink a let him take his nap. Sometimes we'd walk around the park with him in the stroller napping, but found that most of the time we liked sitting down and having a break too. Some kids need to go back to the room to settle down and take a nap. Whatever it takes, don't skip normal naptimes. We also made sure we got to bed pretty close to normal time each night. Stayed a little late one night, but sort of paid for it the next day.
Good luck, have fun, and take it slow........