I've been doing Low Carb since 2002 and have never had a problem at Walt Disney World -- BUT its not readily available as some might think, and you need to look at your options. I'll see if I can find a breakdown of what I really liked where, since I wrote it down once...but here's so info based on my 2-3 trips per year...
Breakfast: Many locations have bacon, eggs, cheese, creamcheese, sausage, ham. Even fastfood places that have "breakfast sandwiches" will work....for example, at DHS, you can get a double breakfast sandwich that comes with a big slab of egg, double sausage patties, cheese...just don't eat the biscuit they serve it on, but its decent size...for bigger size appetites get two...There are some breakfast buffets -- in the food courts, all snack products are available, including things like salads and egg salads and similar in their coolers. I have found that breakfast is absolutely the easiest meal of the day to do low carb at WDW. the caveat: you have to get up early and not sleep in, otherwise you'll be eating while others are already at the parks.
Lunch: Is the singularly hardest meal of the day to do low carb unless you go to a sit-down location, or don't mind salad every single day. There are salad entrees at every major counter service restaurant throughout the parks -- Lunch tends to load on the carbs because they are cheap and plentiful...For those not in the know, fruits are NOT low carb -- you can not substitute apple slices for fries,,,,you might as well be eating the fries, its the same number of carbs. Also in general avoid ANYTHING at WDW that is market as "no sugar". They use a ton of carbs to up the flavor quotient on anything that they do not use sugar in, so avoid those. They are carb bombs. The various buffets around the parks are the best bet. Almost all the sit-down restaurants can prepare your meal low carb (Yak and Yeti is one of my favorites, and they even send the chef out to the table to meet you and get your approval on substitutions they might make in your meal to make it low carb. Hotdogs (don't eat the buns) and hamburgers/cheeseburgers (ask for a fork) are plentiful throughout. I bring some atkins bars with me in my backpack to fill out the dessert quotient of my lunches...there are no lo-carb desserts anymore in the parks. Back 10 years ago when Atkins was popular, the ice cream stands had low carb options. This is no longer the case.
Dinner: is the same as you might have at home. Choose wisely, and be careful of the sides. THere are plenty of great entrees and salad-based entrees that are low/no carb. Just like at home, you can make high-carb meals into low-carb meals by removing the bread, pasta, rice, corn, breading etc. Turkey legs are large and tasty (though very messy and very very salty if you are watching salt intake). I find that I can not eat the turkey legs because they have so much salt in them I get dizzy almost instantly.
Approach your trip to WDW the same way you approach a day out at home meal-wise and you will do fine with low carb choices.
My only complaint: you will find yourself picking things out of almost all of their pre-made salads-- they all include something high carb that will need to go (berries, or tortilla strips, or apples/pears, or crutons, or onions.)....
