Lots of good tips and suggestions already but I just wanted to let you know that you are in good hands at WDW. Disney has made traveling with allergies a breeze. My son has a severe nut allergy and I am severely allergic to cold cuts and a spice called Anise. We've been going to Disney for over 10 years and never had an incident. The chefs have all been wonderful and even when we go to buffets, the chef brings out a plate from the kitchen just for us to make sure there are no risk of cross contamination. There are allergy free menus at each restaurant now so need to speak to the chefs anymore unless at a buffet. I suggest you indicate a peanut allergy on your ADR beforehand. When you get to the restaurant mention the allergy to the hostess.
When planning a WDW trip, I always pre-order breakfast items and snacks from Garden Grocer and get it delivered to the room on our arrival day. I usually get Multigrain Cheerios which are nut free and Enjoy Life cookies and some fruit, cheese and drinkable yogurts. I usually pack in my carry-on some granola bars. I like Made Good granola bars which are nut free and healthy too.
There are tons of snack stands that serve nut free items in each WDW too so no need to panic. My son loves dole whip and he was even able to eat churros last time. I checked the allergy book at the snack stand and they were free of nuts! Always ask to check the book as ingredients change. Disney restaurants always have ice cream sundays for the boys that are peanut/nut free. I suggest you look at the menu before booking any ADR to see if there are a lot of nuts present in the restaurant. If so I personally would avoid the place and pick another restaurant, there is so much choice at Disney.
Last trip, we attended the
MNSSHP and my son got a bag full of peanut/nut free candies. He got "Sufsweets" gummies and jelly beans, "Enjoy life" chocolate bars and something else (cannot remember). He was a happy camper and it was a fun party to attend.
I know what you are going through. It seems so overwhelming at first when your child is diagnosed. Even though I have food allergies, when my son had his first allergy, I felt so helpless. I lived with food allergies since I,m a kid but still, when its your kid, it is still hard to accept. Once you find the brand names that are safe for him to eat, it will get easier and you'll feel less overwhelmed. My son is now 10 y.o. and he carries his Epipen around with him and is really careful before eating any food. He usually asks to read labels at his friend's house. It wasn't that easy when he was younger, because I had to be the one looking out for him. I called ahead before he went to birthday parties. I had to show others how to use the Epipen when I left my son anywhere. Family had to change how they cooked and handled nuts in their homes if they wanted to babysit. Bakeries are to be avoided so I always bake a cake and bring dessert when we are invited anywhere to make sure my son can have dessert. It takes more effort but in a way, its not something that cannot be prevented. The Epipen is extremely effective at stopping an allergy. I always told my son, accidents might happen and you might get an allergy one day, that is why the important thing is to have an Epipen on you at all times. If you have the Epipen, your safe.
Don't worry about travelling with a nut allergy. We have traveled all over the world with the boys and never had any problems. It just takes a little more planning and more effort but its doable. I am extra careful, carry food in my luggage that I know we can eat. Always call a restaurant before going to make sure it is allergy safe and speak to the chef once there. Nut allergies are so common now that everyone is aware.
Hope that helps.
Have a wonderful trip!