I am anaphylactic to milk, peanuts, tree nuts and seafood. One of the reasons we cruise with
DCL is because of how well, in our experience, they handle food allergies. We have sailed on the Dream (3x) and Fantasy (1).
I have posted on these forums previous about our food allergy experience with DCL:
http://www.disboards.com/threads/special-dietary-requests.3398539/#post-53417650 That whole threat (and others) has some excellent info.
I will add: on our last cruise, December 2015, a B2B on the Dream, I pre-ordered all of my meals (breakfast, lunch, dinner), not just dinner, the night before. Most of the breakfast and lunches we did in the MDRs, but a couple times we did ask if it would be ok to have it in Cabanas and they said yes. so, when I arrived at Cabanas I just let one of the head servers know I had pre-ordered an allergy meal for there and they took care of getting it and bringing it out to the table i had chosen. This worked well for us, though for the most part I preferred eating in the MDRs.
I have gotten snacks at the QS restaurants on the pool deck -- safe pizza, chicken fingers. I think I got a burger on one of the trips. Fries. But you have to wait and it takes longer. A manager or chef will take the order and prepare the food. You have to wait until one is available. It is VERY VERY loud around that area due to all the guests around, many of whom are talking. So having the conversation with the manager/chef can be challenging. Then, they have to prepare the meal. I only did it when I REALLY wanted something (special, like the pizza) or when I e.g. needed food to tide me over to late dinner.
That said, the MDRs are the only place they definitely can make safe food. The QS places may or may not be able to -- much of the food isn't even prepared there it is prepared elsewhere, and there isn't a lot of space behind the scenes at the QS places. Something like the pizza was doable because the pizzas are made "from scratch" (well, to a point: the crusts are pre-made, the sauce is pre-made, etc. But all of it assembled together into a pizza at the QS place). So the chef was able to clean a workspace and his hands, use aluminum foil as a safety barrier, use an Udi's crust (those have egg for those of you with egg allerguies), their normal sauce and pepperoni, and some Toffutti "American cheese" slices (fake cheese) to make me an AWESOME pizza. But I would never expect that a QS place could e.g. make me a safe wrap sandwich. They had allergy-friendly chicken fingers (very similar to the ones served at WDW restuarants), so again, something already prepared it just has to be cooked. They did not, for example, have the facility to take a raw chicken breast, prepare a batter, and make a chicken finger actually from scratch -- but the MDRs could do something like that since they have the raw ingredients on hand and a real kitchen.
I also brought some safe foods on board with me, which we were glad we had. For example, the time I took a nap and slept through lunchtime... Did I mention we have late dining ?
Finally,
ALWAYS VISUALLY CHECK the food you are given: does it look "right" ? Pull apart each layer of that hamburger to make sure no cheese is hiding, etc (as apporpriate for your allergies). Mistakes DO happen. They happened to us -- fortunately, were caught by myself and the server at the same time immediately after I was served and before I ate -- because I visually checked. A wrong plate can be grabbed, other mistakes can happen.
One more point: the risk of cross contamination or hidden ingredients at the buffets is very real. On one of our cruises, my sister (who has what we had thought was a mild seafood allergy) ate lunch from Cabanas, choosing things that should be safe for her (no seafood!). After lunch she was tired and a little bit itchy but didn't think anything of it. She came back to the stateroom and took a nap. When she woke up from the nap, it was clear she was having more than a little allergic reaction. Off the medical centre we went. They were great. But not how we wanted to spend part of our cruise ! We still don't know what the offending food was, but no more buffets/lunch at Cabanas for her.
SW