After having more than one unexpected detour/delay and loss of luggage when flying cross country, I was more cautious than most when flying with my kids when they were little.
I always packed an entire day's changes in clothes, blankies, diapers and a whole can of formula with two good bottles of water. (And at least two extra nuk's!) As they got older, I added in a small soft sided cooler with munchies and snacks. I still make sure that they have their bathing suits packed in their carry ons now. That way, if nothing else, they can hang out at the pool!
When they were little, I frequently traveled on my own with the boys. When I traveled with my DH, we would actually bring a duffle bag with the rice cereal and baby food jars. Now days, they have the plastic ones which will make traveling a whole lot easier! When I traveled to my parents, they purchased much of it before we got there. When I traveled other places, I ordered online at Albertsons or something similar, so I'd have the baby food stuff that we didn't bring on with us.
A couple of "gadgets" that I Loved when traveling with infants, and in particular that we liked at WDW. First, I purchased one of those car seat cover/carriers. LOVE it. More than 11 years later, we're still using ours, though it's definitely taken a beating! The shoulder strap enables us to easily carry the car seat around. We always gate check (see note above about being re-routed more than once!). You can also toss in jackets, blankets, etc. into the extra space within the carrier. If you're getting your baby a seat, then you have all the stuff with you without having to find other space for it. It's not counted as a carry on even if you do bring it on.
Another thing we got, specifically for our first WDW trip with our oldest son was the completely collapsable/take apart portable chair. I think of it as a highchair kind of thing. This was a godsend for us when we were trying to feed him breakfast or afternoon snack, it confined him to a limited space. There was more than one time that we put him in the seat with books and toys (he liked to sit up) while we got ready.