It's hard to travel with children who have severe allergies, especially food allergies. There are only so many allergy-free foods you can bring along, and most places won't let you prepare your own foods (even if you could be assured that the plates, pots, and pans don't harbor traces of dangerous ingredients). We had heard that Disney was good with allergies, and we found a travel expert who specialized in helping families with children with allergies (yes, there are such people!). That made it so much easier for the 15 of us to enjoy our voyage.
We spent a couple of days at Disney World before the cruise, and I highly recommend that if you can work it into your schedule. It allowed us to go on the cruise relaxed and vacation ready. The staff at the Grand Floridian, where we stayed and ate all our meals, went out of its way to ensure that we would have no allergy problems. The servers checked ingredients for every dish before serving it.
That care extended to the cruise line.
We had four adjacent cabins, with connecting doors in each pair, and the option to open the balcony dividers so we all could go from room to room without going into the halls.
The rooms were surprisingly spacious, even when we had four children and two adults sleeping in them (although the kids switched rooms and beds most nights as they paired up with different cousins). A clever heavy drape separated the "adult" side of the room from the children's side (which had bunk beds and even a Murphy bed) so we could put the kids to sleep and stay up to watch television or read.
Storage space was generous: we didn't fill half the drawers and shelves.
Nice trip out on the water, tame travel, fun to feed the fish, interesting stories from the captain and his mate.