I have been taking my DS since he was 10 mos old. he is now 4 yrs old. I put in the diaper bag;
a few juice boxes, crackers, cookies and lollipops. This way I always have something on hand.
I would also take a small toy that they like to keep them occupied when needed.
If you going when it is hot, take a change of clothes or a bathing suit and sandals, there are a few spots where they can get wet.
I learned the hard way, when my daughter was 4 she got wet at Ariel's Grotto and she stayed wet with wet sneakers all day, Thankfully it was warm out, and it took days for the sneakers to dry all the way.
So when I went with my son, I carried a bathing suit and water shoes for him, so he can play in the fountains.
Also if it is hot I took a hand towel from the room and wet it through out the day to wipe the kids face and hair when it was getting too hot out. It really helped when we were standing in lines.
The only thing I did that was overboard and I never needed was carrying to much medince with me into the parks. Lesson learned, just carry something for a fever and something for a headache for the adults. I think I took the whole medince cabinet.
And if you ever need anything for the baby or sick child go to the baby Changing Stations, there is one in every park, they have anything you might need, Medince, diapers, microwave, rocking chairs, TV and changing tables.
My son got sick all over himself and I took him there to change him, they had a nice size sink I sat him in it and washed him down and bought him medince and calmed him down so I could get back to the hotel.
It can get crazy thinking what you'll need but after you do it, you'll know what you will need the next day and what you won't.