My ODS will be five in a few weeks. He's allergic to wheat, barley, rye, eggs, peanuts and tree nuts. My YDS was allergic to dairy as a baby, but outgrew the allergy at 13 months old. You've gotten some great advice so far. I wanted to add a couple of things that I didn't see mentioned:
Replacing Eggs: When you need to replace an egg, you need to figure out whether the egg is for binding purposes in the recipe or for rising purposes. If an egg is used just for binding (like in pancakes), then you can replace the egg with a heaping tablespoon of applesauce. If it is for rising, or for both binding and rising (like in a cake), you need to try a different sub. For a cake, you can use a boxed cake mix (make sure that it is dairy free), and replace ALL of the ingredients with one can of soda (clear soda for white cakes, and darker soda for chocolate cakes). This is a SUPER easy way to make a cake (this works best with cupcakes b/c they have a smaller surface area to rise in). You can also buy powdered egg replacer at Whole Foods. The stuff is not my favorite, and usually only works replacing one (maybe two) eggs in a recipe). Our favorite egg replacer is flax seed (someone mentioned this one, I htink). We use one tablespoon milled flax seed to two tablespoons water for one egg, then we microwave it for 30 seconds-- it turns to a gooey mess, just like a real egg. The flax seed will work as a binding agent and a rising agent.
Finding a bread: If you stick in the bread aisle for long enough and read enough labels, you will be able to find a safe bread (and probably safe hamburger and hotdog buns, too). There used to be a variety of Sara Lee bread that was dairy and egg free, but manufacturers do change their ingredients all the time, so you'll just need to hang out in the bread aisle for awhile until you find a safe bread.
Margarine: Fleischman's sticks and Fleishman's light in the tub are dairy free. You can use the sticks in baking.
Neither rice nor soy milks are nutritionally equivalent to whole cow's milk. Both have far less fat, which a 1yo needs for brain development, and rice milk has virtually no protein. Rice milk is a great substitute for cooking and the occasional drink, but is *not* a good one-for-one substitute for whole cow's milk for a young child who had previously been drinking large amounts (more than a few ounces a day) of cow's milk. Think of it as the equivalent of apple juice - mostly carbs.
Assuming that he's getting enough protein from the rest of his diet (and I'd do a food log for a week or so to verify that, if he'd been getting a lot of nutrition from cow's milk), and it's mostly the fat to carry him through the night, try adding a tablespoon or two of coconut milk (neither nut nor milk!) to the rice milk. It's very high in fat, and tastes good. If you need to supplement protein, too, until he's eating more high-protein foods, you can get rice protein powder at a health food store.
My DD reacted to dairy and wheat when she was a baby, so I had to eliminate those things from my diet. (Most kids don't react to mom's diet. Mine did.) She was breastfed though, so had a reliable fat/protein source until she outgrew her allergies. That took about a year.
ITA-- Your LO may need soy milk for now or an adjustment in his diet to make up for lost protein and fat. Rice Milk will not provide that like cow's milk does.
Someone mentioned sunbutter. I have been a little unsure about using it with our two year old as I was afraid he might confuse it with peanut butter and eat that if he had the chance. I would love to be able to do a sunbutter and jelly sandwich for him. Anyone have these concerns and are they valid or will it be fine??????????
We've used Sunbutter with my DS since he was about two. It can be a choking hazard, just like peanut butter, so I wouldn't introduce it until you would "normally" introduce peanut butter. DS has never had a problem differentiating between the two. We are careful to call it SUNbutter and talk about how peanutbutter is not safe but sunbutter is. We also have a book called Ellie the Allergic Elephant. It is about an elephant who is allergic to peanuts. It's very cute and helps the kids to understand.
I had an array of food allergies growing up - many causing reactions to my breathing and skin. (Egg whites and yolks, milk, peanuts, chicken, rice, and corn to name a few.)
I don't know if doctors discussed any "treatment" options with you other than avoid the food at all cost. This is NOT what you asked and you didn't share, but if you know the severity of the allergy that would certainly be beneficial. There were certain foods that I had to avoid and some I could have as long as they were in cooked items (I couldn't not eat eggs, but could have a muffin made with egg.)
When I was little (I'm 37 now) my family was in the military and rarely lived on base, so my mother usually took the advice of the locals, more than the military doctors. So, in addition to avoiding the potentially harmful foods, she also gave many of them to me daily in very tiny doses - touched the peanut everyday forever then got the dust on my tongue, etc. (I still eat three peanuts in the morning and before bed

) I do NOT advocate this, but essentially, she was building my immunity. After we moved stateside, I started allergy shots. The doctors couldn't believe the change in results from two years previous. They swore that the ratings of my allergens were in error - they were still there, but mild (hence started the allergy injections).
I also showed improvement with these too. I began eating PB&J nearly everyday in high school. Still love it.
I stopped allergy shots about age 15. I'm back on them (6 months ago) because of a new shrimp and tomatoe allergy (and don't forget the never ending pollens). I'm hoping it works as well. (Sorry to highjack your post.)
Anyway,

to you and your DS. I hope it's only temporary.
There are studies going on right now where they are giving kids increasing amounts of peanut flour to desensitize them to the allergen. Like you said, though, it should only be done under a doctor's supervision. I'm interested to hear more about your shots for FA's. It was my understanding that in the US shots for FA's are not given. DS is currently on shots for his environmental and seasonal allergies.
DD2 is allergic to nuts and egg. We aren't sure about shellfish so we just keep her away from it all. We have 4 epi-pens just in case something happens!
Anyway, by chance we have figured out she can have egg if it's cooked into something like a cake, but not straight, and nothing like egg noodles. She breaks out but doesn't go into shock.
We have also figured out accidentally that she can have peanut oil - I took her to Chick Fil A and didn't know they used peanut oil and she was fine. In fact I talked to my friend who is also allergice to nuts and he said he can eat peanut oil and always has. DD can also have stuff that is manufactured with nuts but nothing that contains nuts. So apparently her allergy isn't as sensitive as others. Thank goodness!!
You'll figure this stuff out as time goes on. It's a lot easier to live with some allergies than others. In fact, the peanut one has been fairly easy. GL with it all!
Some kids can have egg cooked into things. The theory is that you are allergic to a parts of a protein in a food called epitopes. Some epitopes are bent over one another (they are called conformational epitopes). Those epitopes are actually destroyed when the food is cooked, so the allergen is removed. If you are allergic to sequential epitopes then the allergen remains when the food is cooked. Unfortunately, there is no way to test which kind of epitope your child is allergic to at this point. The only way to find out if your child can handle eggs in baked goods is to do a food challenge, which should be done in your allergist's office.
Also, highly refined peanut oil (like that used at Chick-Fil-A) does not contain peanut protein, so it is safe for the vast majority of peanut allergic individuals. My DS gets hives if he even touches a small amount of peanut butter, but he eats chick-fil-a with no problems. Some peanut oils are not safe-- they are the cold pressed or expeller pressed peanut oils and are usually considered "gourmet" oils. If I don't know what kind of peanut oil was used in a product, we avoid it, but Chick-Fil-A publicizes that they use highly refined peanut oil, so we let DS eat there.
Boy, I just wrote a novel!! I hope some of the info was helpful! --Katie