Don't the menus say "for our younger guests" rather than "for those under xxx age"? Anyway, when I was first pregnant with my son (about 3 months along) I was so nauseous and couldn't bring myself to eat certain/most things. I ate almost exclusively off the kids menus our entire trip (I literally ate mac n cheese at least 1x day!). . . As pp's have said no problem at counter service places, and table service places I simply told them my situation and it wasn't an issue. I don't remember what I was charged, but it was definitely a kid's size portion. We ate at Chef Mickey's that trip and I paid adult price, but stuck with the kiddie counter (and a handful of shrimp, surprisingly enough that didn't make me want to barf LOL!) 
