I am sorry that you have found about this.
But I just wanted to let you know that I am in my late 30's and I have had a life threatening peanut allergy my whole life. Your daughter will grow up knowing no different and will grow quite acustomed to avoiding peanuts, like it is second nature. I check all labels of everything I buy (and everything my family eats as we do not have anything containing nuts in the house as I only need a tiny trace to have a reaction, I have even had a reaction from inhaling steam from a satay meal), I don't even think before reading a label, even if I have been buying a product for years, I still just pick it up and read the label, don't even realise I'm doing it.
As far as travelling to WDW with a peanut allergy. There is no better place in the world to travel with an allergy. I have travelled all around the world (just came back from
Disneyland Paris which was a nightmare with it came to food) but WDW were AMAZING. When you eat there at TS restaurants, the chef will come out and tell you what is safe and what is not safe to eat off the menu or buffet. If you make an ADR then mention the allergy and the chef will have you in his notebook by the time you have arrived and be prepared, but if you don't make an ADR, it's still no problem, just tell them when checking in about the allergy and they will get your server to bring the chef out. You can also email Disney before and they will email you a list of safe snacks that you can eat around the park (I think it was them who emailed it, I may have found it on a forum/board)
I advise on removing all peanut products from your house, that doesn't just include food. You must check your lipsticks, sunscreens, makeup, shampoos, conditioners, moisturisers, many of these products can contain peanut oil. Everything, you need to check the labels on EVERYTHING. There are a lot of funny names out there also for peanuts, Arachis Oil, Loramine Wax, Peanutamide, Food additive 322 lecithins, and I think there are some more. Wipes are very handy to carry all the time too.
I do not eat M&M's of any description. Do not eat anywhere without asking what oil they cook with, peanut oil is becoming very common in cooking and not just in asian restaurants. Do not eat anything for that matter without checking the ingredients, if you get an "I don't think so" at a restaurant, ask them if they would mind checking with the chef. I believe in America there are many websites that sell peanut free products. There is a good board
www.peanutallergy.com they have a forum and there are many parents there with kids with PA. But just know that it is certainly scarier for you as the parent that it will be for your daughter when she is older and able to take control of this herself. It's hard, well I don't find it hard (because I have grown up with it), but it will be hard to totally remove something from your life that you are used to having around and learn to avoid it, it will be hard until it becomes that way that you don't need to think, before it becomes natural to be peanut free, which sounds a bit strange but there may be times that you will pick something up and not think for a minute then remember "oh peanuts, and check", but there will be a time and certainly for your daughter will grow up not knowing any different being two, when you won't need to remember, because avoiding and checking will just come naturally.
Anyway, all the best with it, enjoy your WDW vacations as they are just so good with allergies.
but he was definite about not eating m&m's, plain or peanut, as even the plain ones probably have peanuts in them.
Now at age five, she hasn't outgrown any of the allergies and they are a part of her daily life. There are still many food options out there. Prepackaged foods most generally are not an option. ALWAYS read labels. Even foods you find are "safe" you need to continue reading the labels, manufacturers change ingredients on a whim so what you buy one week could be different the next. After awhile it will become routine and you WILL feel less overwhelmed. 
