I would advise you to stay away from the soy milk. Soy is a well-known allergen, and it's NOT health food. http://search.mercola.com/Results.aspx?q=soy&k=soy In fact, soy is downright dangerous. I don't think it's a good idea to give babies and small children soy milk, especially if they already have these allergies you're talking about. The other information about what amounts to vegan recipes is a great idea. And, I know where you can find some of these vegan recipes that are normal foods. There is a great website called care2.com. Just go to healthy living and search the recipes. You can specify vegan recipes. The majority of their recipes are vegetarian, but if you take it one step further and go for the vegan recipes, you'll be able to avoid the dairy and the eggs. Or, look at the vegetarian recipes that call for milk and substitute with the rice milk.
I would suggest going easy on the eggs, eventhough they're not actually dairy. Your daughter isn't allergic to them, because eggs aren't from lactating mammals. But, eggs are a common allergen and that allergy is on the rise. There is a link to this with the use of vaccines. This information is also on mercola.com. I'm not full on allergic to eggs, but I still can't eat them myself, because they still make me sick. This is called a food sensitivity, since it's not anaphylaxis.
About the goat milk, you probably can do that. My aunt got a goat to use when my cousin was little, so they would have enough goat milk available all the time. He is a lot younger than I am, but he has his own children himself now, so obviously raw goat's milk didn't hurt him. There is some important information about dairy intolerances on mercola.com, too. The laws requiring pasteurization are actually causing all the friendly flora in milk to be killed. This is one of the reasons why many of us are lactose intolerant, which is still not any fun, even if it's not anaphylaxis. If you're able to find a local supplier of raw milk, especially goat milk, you might want to consider that. There are certain laws that will allow local suppliers to sell it to you raw, but they can't sell it across state lines.
p.s. I assume you have checked bookstores and library. You may also want to look into vegetarian cookbooks as alot are recipes with no eggs or milk. There is also alot of goat cheese available to.
Allergies. I am new to this sight so hope I do not over step my boundaries. I do know that my baby brother had alot of allergies and was really premature. The hospital basically sent him home to die at 3 lbs. Medical science wasn't like it is today. Anyway my mom gave him goats milk and mashed bananas. He lived to a healthy 37 yo when he died of cancer. As with any suggestion you may want to check with pediatrician.
Hi ! Has your daughter tried rice or soy milk ? If not, those are two options that you may want to discuss with her physician.
Also, I would highly recommend considering purchasing a homeopathic supplement for dairy allergies. It worked for my husband's allergy to dairy (he used to get welts !) and may work for your daughter. Of course you should also discuss this with your daughter's physician and if your daughter has a severe allergy to milk... you shouldn't reintroduce milk to her. But at least if you try homeopathy and she accidentally drinks milk... you may find that her allergy is gone or her allergy reaction has significantly decreased.
Good luck !