I took my son when he was nine months old and we had no problems. A few things we did:
1 - We made sure to let our son get down on the ground and crawl around and push the stroller. We'd find out of the way places for him to "roam." We wanted to make sure he wasn't confined to his stroller all day. We also let him play in some of the water play areas if it wasn't busy with lots of big kids. We were there in Sept, so it was still hot. Not sure what the temp is in Jan.
2 - We have a Mac Triumph and he was very comfortable in that. Napped off and on throughout the day. We didn't return to the room. Another great place for babies to nap is the WedWay People Mover/Tommorrowland Transit Authority (most times you can just stay on and go around and around). We spent a lot a time on this ride over the course of our vacation - but it was one of our favorites pre-kids, so that fact we had an excuse to stay on and do loops was great for us!
3 - I prepacked food for each day in separate ziploc bags. So for each day I had two snack size zip bags of premeasured dry cereal and two containers of baby food in a Ziplock bag. My son was eating one container & cereal per meal. I'd get a bowl or cup where ever we were eating and juice to mix with the cereal. In the morning before heading out I'd just grab one of the bags, throw in a spoon & bib and go. If you want you could pack a disposable baby spoon in each of those as well. I was nursing, so I don't have any formula suggestions if you are using formula. I had no problems nursing, there are lots of other threads on this topic.
4 - We were on the dining plan when we went and there were several sit down meals where my son had had enough by dessert so to speak, so one of us would take him out to roam and the other would get dessert to go and "pay the bill." Most places were very accomadating. Also, we would try to order apps and meals at the same time to move things along.
5 - Our son had no problems being scared of anything. He enjoyed just looking around and checking things out. We did avoid doing too many shows just because he was not into just sitting, just too squirmy and shows just don't keep a 9 months' interest. We did a few, some he was fine others he was going back and forth between everyone in our travel party.
6 - Our son was not a "carrier" baby. Hated them after 4 months. So we just carried him in lines and on rides. He'd just sit on our laps while riding. The main ride I was a little leary of is the Safari because it is so bumpy. I just made sure to sit in the center and held on tight. He was fine.
7 - In the security lines, we'd have nothing (but for son) in the stroller and one person would take son & stroller through the non-bag line and then the other would take the bags through the check. And we tried to pack light in the parks. I took two bags. A "diaper bag" that fit in the basket of the stroller. This had a change of clothes, my ziplock bag of food, spoon & bib, a sippy cup (for water and occasional juice), a receiving blanket (to cover up stoller while baby was napping), one cloth diaper - for potential clean ups, and extra diaper & wipes. My baggalini carried normal park stuff (camera, etc) plus 3 diapers, wipes, and changing pad. At meals I'd restock diapers if necessary from the diaper bag. I usually had one toy linked to the stroller for the day and that was all. My son was really not into playing with it anyway. To much to see.
Hope some of the suggestions help. Have a great time!!!
Oh - and take a hat!!!