We've done two Disney cruises with my younger son who is anaphylactic to peanut/tree nut/shellfish and he is also a type 1 diabetic.
I think much like the parks, your experience is somewhat dependent on the people you must deal with when asking about the allergies. On our first cruise the dining room manager (he is not the chef or the servers - I cannot remember the exact title) said that nothing could be guaranteed except what the chef actually prepared from scratch - but they wanted to make him things like plain chicken breast, plain rice, etc. He definitely did not want to eat like that. I had to get into the discussion about the labels and may contains and manufactured in a facility and all that. He was somewhat annoyed with me (and me with him) - but he ate the usual kid fare (like chicken nuggets, etc) with no problems. He was able to eat from the lunch buffets and from the quick serve places near the pool.
Our head waiter on this past trip was much nicer and I felt like she understood the food issues better. They had TONS of Divvie cookies for him which was great.
I am saying that I would not hesitate to take a food allergic child on the cruise - they can definitely deal with it. The kids club will keep the epi-pen and all of that and they are good about hand washing. Do the medical form a few weeks in advance so you will get a call from them.
Have fun!
