We went last February with our 3-year-old and our almost 3-month-old. We had a great trip.
She was supposed to be 12 weeks but she was born almost 2 weeks late, which meant traveling with a younger baby than expected -- something to keep in mind.
In our case, we traveled with 2 sets of grandparents, which really helped. We stayed in connecting rooms with my parents on the monorail (also a huge plus).
I think cooler weather is better than hot weather with an infant. That being said, we had very cold weather and I wished I'd brought a winter hat for the baby and a fleece suit/jacket. Luckily I had a sleeping bag/bundle me thing for her stroller. Just keep in mind that temperatures fluctuate wildly at that time of year.
Although we flew, my parents drove down and were able to haul some baby gear for us. We used our own pack 'n play to reduce germs, but also because I wanted the change pad attachment, diaper caddy etc. so I could have an entire "baby station" in the room. I was nursing, so bottles weren't a big issue. I packed a ton of stuff for the baby but still needed to do laundry.
We took two separate strollers. I was happy with that choice because there were several times when I needed to visit the Baby Care Center (those are fabulous) and didn't want my older daughter to miss out on an attraction. We were able to split up. The baby's stroller had a full recline for napping. I added a Ray Shade for extra sun protection (it was cold but sunny!). I also took my sling (remember a sunhat because the sling won't shade baby's head). She only went on a few rides (there was usually somebody who wanted to sit out with her and I wasn't going to wake her if she was sleeping).
She was still waking to feed 2 to 3 times per night, so I was quite tired. I think I was asleep by 8:00 every night! You have to go slowly for the children and for yourself.
Most days we took an afternoon break and had lunch at our resort. It was hard to schedule a break at HS though because we were working around show times. We decided to stay through lunch. I booked a TS lunch at Sci-Fi Drive In and was so glad I did. It was far less hassle than trying to organize everybody at a CS location and it was dark and quiet in there. It was a very calm break in our day and the baby slept through the entire meal.
The CMs will let you bring your stroller into restaurants if you tell them the baby can't sit up yet (assuming you aren't bringing a tank). Some restaurants (Crystal Palace, 1900 Park Faire, Chef Mickey's and others) have infant highchairs with a reclined back. In one restaurant they brought me a clean table cloth to drape over it before placing the baby. In others I just covered it with a receiving blanket. The baby enjoyed table service restaurants, although we made sure (a) all of our reservations were early; and (b) we didn't have to travel to get to the restaurant. Mostly we ate at our resort (one of the reasons I picked the GF -- so many restaurants close at hand).
You have to be flexible and always willing to scrap your plans and tend to the baby. You will miss some things your older child is doing, but you will have a great time.
