We have sailed with Disney 4 times, on the Dream and the Fantasy, so I cannot speak specifically to the Wonder. However, all of our servers and head serves have been excellent.
Some advice:
You have already noted it on your reservation, but I suggest doublechecking with
DCL that it is listed. Have them read back to you what they have noted.
When you board the ship, in the Navigator it will list a time and location where people who want to make dining changes should go. Go to this. Explain you have food allergies/sensitivities (whichever it is) and that you want to make sure they have been noted and everything is good to go. They should read you the list they have noted. Also, you can ask them if the dining team you are assigned to is really good with handling food allergies/sensitivities. Each of our cruises I have not had to ask, the head server we were meeting with volunteered that the team was very good with allergies. On our first two cruises, at that dining session we were also shown the menu for dinner that night and placed out order then -- this gives them time to prepare alternatives. THe third cruise they did not do this and it meant fewer options at dinner. I prefer to pre-order during the dining session if it is an option.
I always carry a "chef card" with me - a 4x6 pale yellow index card on which I have printed my food allergies and a reminder about cross contamination. I modeled the wording on suggested wording I found online (there are many places that have chefs cards now). I used Word to create it and print it. I am on about version 6 or so as I have tweaked the wording over the years. I print a bunch of them and carry them with me whereever I go. I also have one I printed onto white photo paper and then laminated -- that one stays with me. The yellow index cards I can give to wait staff or chefs and they can keep them as I have more.
On the first MDR dinner, I show the yellow card to our waiter. They have always already known my allergies, but they take the time to read it.
Each night in the MDR, we have been shown the menu for the next night's dinner and ordered then -- this gives 24 hours for the chefs to come up with alternatives and means many more things are possible. Our last cruise we also ordered lunch and breakfast them, letting them know which restaurant and about what time we expected to go for those meals. This allowed things like eating breakfast at Cabanas -- my preordered breakfast was prpeared in the back while my sister could do the buffet. Also, by pre-ordering I could get allergy safe Mickey Waffles every morning

Our waiter would tell us what restuarants they would be working the next day for beakfast and lunch and we usually chose the same ones, though not always. For
Castaway Cay day we preordered lunch and they let us know which Cookies to go to to pick it up and between what times.
I found the DCL app on my smartphone very helpful -- I could read all the menus for the entire cruise at any time. This helped quite a bit with the pr-ordering each night: I had already read the appropriate menu on my phone and knew what I wanted, so reading the paper menu was just a quick check and then order. It made it go much faster than pre-app when we would have to read the menu and decide after dinner. This way it was a fast confirm and order.
Dining in MDRs is recommended for those with food allergies and sensitivities as it is much harder and sometimes impossible to provide a safe food at the QS locations on the pool deck. HOWEVER, I have discovered at least on the Dream and Fantasy that there are still some options at the QS locations if one gets hungry outside of meal times. For example, there is fresh fruit. There are sealed bags of potato chips. They had allergy friendly chicken fingers and could make me safe fries (dedicated fryer) in the hambuger QS. And at the pizza QS the chef was able to make me an amazing personal pizza using an Udi pizza crust, normal pizza sauce, normal peperoni, and Tofutti cheese slices. I was able to watch and he cleaned his hands and work area and hands again, used aluminum foil as a shield under the pizza, and he showed me the containers of the pizza crust and tofutti cheese so I could verify the ingredients. these may or may not be an option on the Wonder, but as I discovered -- without ASKING you never know
Finally: I bring some safe food on board as a fallback option. On our first cruise, I accidentally slept through lunch one day. Oops. But I was STARVING when I woke up and at the time did not know that the QS could make something safe. So, I tucked into some of the safe food I had brought on board. I still bring safe foods, but now I also know that Qs can be a limited option if they are open.
For excursions: some excursions will include a meal. We try to just avoid ones that do, but we have had a couple that did. We spoke with special services at DCL well in advance of the cruise about whether the excursion provider would be able to accommodate my allergies. DCL was able to speak with the vendor and confirm that they could and what I needed to do action-wise on the excursion to ensure I got safe food. Both times it worked out fine, though took longer to get my food (so build that extra time in).
Find out what the rules are at each port for bringing off and on food. At the very least it will have to be commercially prepared, factory sealed products. Some ports do not allow ANY food off the ship. Others will allow a restricted list. When food ia allowed I will bring things like a couple squeeze pouches of apple sauce and a couple Enjoy Life bars -- enough to tide me over should safe food not be available when I need it.
SW