i can offer you a little insight from the other side of the needle - i have been type 1/jd since i was a small child.
we had full national-lampoon style vacations most years, and i never minded my mom watching me like a hawk for the first couple of days as we all adjusted to vacation schedule. what mortified me was her telling waiters, hotel clerks, strangers in lines, etc about me and my issue. for a kid 10-16 the most important thing is to not be singled out. i learned to eat my hot dog without the bun or to order a piece of grilled chicken or a salad in order to earn from my body the ability to eat an ice cream or cookies. i learned after a few mistakes that the ultimate cost of eating too much carbohydrate for lunch or sneaking in a sweet treat i didn't arrange for was that i would feel like crap later. having a high blood sugar never hurt me in the grand scheme of things, but after being allowed to make those mistakes here and there i learned fairly quickly to consider other options. i also carried my own stuff - monitor, insulin cool-keeper thing (about the size of a dayplanner, it has these tubes you freeze and slide into the pockets to keep the insulin cold), glucose tablets, cake icing tubes, two or three pairs of fluffy socks for changing, etc. i think over the years this sort of taking ownership of my responsibility for my body and my own wellbeing helped me to gain and keep control of my situation.
i can offer a little bit of disney-specific advice.
never underestimate the mileage. i was a very active kid, but the sheer extent of the walking during a day at the parks threw me for a loop more than once.
the general excitement of a disney vacation can mask signs of an impending low blood sugar, but sometimes we girls do cry or giggle just because.
foot inspection sounds silly to a kid. but i once picked up a rock in my boot while the family was hiking that cause a very minor injury which i didn't notice because i didn't check - and it became something much more serious and inconvenient that it ever should have. disney is nothing if not a pedestrian experience, and our feet are our friends.
heading to the pool in the afternoon can be problematic as the nph from the morning dose kicks in in a body which has already burned breakfast and lunch. i had full-on low blood sugar episodes a few times around the pools in the mid afternoon.
dr pepper works faster than almost any other soda in a sugar-now situation. i think it is something to do with the purity of the corn syrup.
the heat can affect blood sugar levels because it can raise the blood pressure and can cause dehydration, among other things. and that nasty sort-of-dizzy sort-of-sluggish feeling you get when your sugar is high can also be caused by heat, so test after rest in a cool place before you add the extra units. this one has happened to me several times, and it always comes out okay if we sit through the tiki birds or presidents or something before we test and adjust insulin, than if we just run into the restroom right then. having high blood sugar for fifteen or twenty minutes isn't really going to harm anyone, but dosing a blood sugar that is about to fall on its own once the body slows down can lead to a problematic low.
bananas are our friends. potassium deficiencies in diabetic legs that cause those horrific leg cramps in the middle of the night are no fun.
wdw is no problem for a diabetic if you are aware of your body (or your daughter's) and i am sure your family will have a fabulous trip!
We have no problems testing in public and we have seen many others do the same thing. In fact, the kids are much less concerned about others "knowing" when we are on vacation than when we are at home. Once, at Chef Mickeys, the waitress noticed them testing and quickly told us about several sugar-free desserts that she could get for us. 
