The youngest I've visited with was when my son was 18 months and we didn't have any issues with the food. All the buffet style restaurants have kid friendly items and there's always food that can be fed to a novice

We just picked the softer, easier to chew items like hotdogs, steamed veggies, mac and cheese etc and cut them all up nice and small for him on his own plate. Most of the quick service style food stalls in the parks carry things that can be modified for the littlest customers as well. We bought a lot of hot dogs, fruit cups, french fries and mac and cheese

Also, we always brought our kid's sippy cups with us as well and would fill the cups with milk or half water/half juice so that our LO's drinks were easy and reliable.
Another option is to bring along any snacks that your LO will def eat and that you are comfortable with. You are allowed to bring in a small soft sided cooler which can be pre-packed with baby's favorite foods. This is especially helpful if your LO is eating baby food from a jar still. I'm pretty sure you can bring baby food jars into the parks, the only exception to the "no glass rule."
Unless your LO has very specific dietary needs I think you will be able to find enough for him/her to eat (although you might have to make sure you read the menus first before selecting a restaurant). Casey's in MK has awesome corn dogs that were a big hit with our littles. Flame Tree BQ in AK has mac and cheese that my kids love as well (this is our favorite lunch spot in AK, mac and cheese for the kids and pulled pork for us

).