My mother was a Type 1 diabetic (in the days before Smartphones and apps that could estimate carbs). She ordered at Disney restaurants (or selected items from the buffet) the same way she would at restaurants at home, sticking to things that were prepared simply, and that she knew wouldn't be high in carbs -- meats (cheeseburger without the bun, grilled chicken, steak), cooked veggies and tossed salads (without croutons or tomatoes, etc.), or adjusting her insulin accordingly if she knew she'd had something a bit "carby" (part of a roll, or some ice cream). She tested her blood a little more frequently than at home, just to make sure there wasn't any unadvertised sugar in things. She even carried sugar test tape with her (I don't even know if they sell it anymore, but it was a little roll of paper tape that turned a different color in the presence of sugar -- it was originally meant for diabetics to test their urine in the days before portable blood testers), so she could test the soda she was served and make sure it was "really" diet. It was a bit appalling how often (not just at Disney, but everywhere) that she'd order diet soda and be given regular, which as you know, is a big deal when you're a diabetic!
I think if you stick with what you know is typically safe, you (or rather, your little one) will have no trouble. Do get a carb-counting app (and if necessary at TS restaurants, make an inquiry of the chef) if you aren't sure about something. Take it slow, monitor blood sugars frequently, and keep all necessary supplies with you at all times in case of a high or low sugar. The physical and emotional rollercoaster of a vacation (the excitement, the weather, the staying-up-late) can affect blood sugars all by itself -- even if the diet is perfect -- so you'll want to stay on top of it. Good luck and have a wonderful trip!