I have been Type 1 Diabetic since Age 10. I'm 21 now. We have spoke to the chefs at a lot of the TS restaurants and they are very helpful. It's different at the CS though. It seems a lot of them are clueless to tell you what the carb count is in anything.
Are you taking shots or insulin pump? I'm on an insulin pump, makes it a bit easier. But before I got on that I swore up and down that I would eat healthy at Disney..yeah...didn't happen. But an insulin pump rep gave me a book called CalorieKing, Calorie fat and carbohydrate counter. (You can get it on the site for like..8 dollars) It helped a lot. It has most of the basic foods in it and allows you to adjust the amount of carbs per portion size. It has helped a lot at Disney.
Another thing you need to take in account though is to test your blood sugar much more when at Disney if you're not used to lots of walking/physical activity. When i'm at work, i'm behind a computer all day. When i'm at Disney i'm walking 3, 4 miles a day. So I had a few lows that I had to keep things on hand.
Also, I would suggest carrying snacks with you that contain carbs and protein in them (e.g. peanut butter, cheese crackers..etc) because it steadies your blood sugar so that you don't have to snack too much between meals.
The chefs at TS restaurants have always been understanding about it and I have used the special hotline they have for dietary requests, but it doesn't really work unless you know what you're going to eat and when. Otherwise it's just a hassle, IMHO.
Also, fridges at all resorts are free for medical purposes. So that you can store your insulin.
Hope all this helps.