My ODD was 21 months old when we first brought her to WDW! I remember asking a lot of questions about stroller naps and what to do about naptime. Every child is different. We tried stroller naps and they just didn't work. So, even though we were staying offsite we drove back every day for a nap in a pack and play in a cool, dark room. It turned out ok because on that trip we had thunderstorms every afternoon. For naps, you'll really need to see how they do and whether they will nap in the stroller or not. Because of the nap situation, we usually went early to the parks, went back to the condo for lunch and nap, and went back in the late afternoon for dinner and a few rides.
I agree with PPs, don't try to take in too much all at once; it's easy for them to get overstimulated. We did ride the carousel many, many, many times. Never mind that we have a carousel at a park near our home... Also, we were able to find space for her to walk/run/play on her own - there's not a ton of options in MK, but we had a great time at Innoventions at Epcot and also just letting her walk with us at various times in future World and World Showcase. We went to Restaurant Marrakesh for dinner and she had a blast dancing with the belly dancer.
Characters were also iffy - she did fine with the princesses, but Tigger, et al., not so much. (see photo below...) We did one dinner at Crystal Palace and that didn't go over so well. It wasn't until the following year when she was almost 3 that the "fur" characters became a big hit. But again, every child is different. We found that visiting the parks with a toddler really forces you to slow down and notice some of the amazing attention to detail all around WDW. I think when we went to AK we barely made it past the animals as you walk in - you know, that part everyone runs past at rope drop. We watched ducks and other animals. At least it was shaded there. You will have a wonderful time!!!
As for snacks and drinks - We used a tommee tippee explora insulated cup that was attached to the stroller with a strap. SOmetimes it was ice water, other times milk. For snacks, we brought raisins, cheerios, goldfish, grapes and a few pouches. Since we weren't usually in the parks for very long stretches, we mostly wanted to keep her hydrated.