I pretty much eat what I want, two sit downs a day and at least one dessert a day and with all the miles you walk at Disney I usually don't gain anything, at the most a couple pounds. I've lost 52 to date and definitely enjoy the delicious food and don't worry about it.
I went on a vacation once where I followed my diet "to the T" and felt so deprived when I came home not to have had any of my favorites, that now I eat what I like, but like I said, we will only have 2 meals a day and then a really light meal or a snack. With all the walking, swimming and general activity in a day I do fine.
You can certainly do it though if you put your mind to it. They do have many healthy choices at Disney World that if you want, I'm sure you will still be able to pretty much find foods on your program to eat.