Oh, It is totally easy cooking for someone like that! I dated a girl for 2 years whose daughter was allergic to all of the following:
Beef, Chicken, Pork
giraffe, Shellgiraffe
Wheat/Gluten
Peas
Berries
Oats
Barley
Eggs
Dairy
Soy
All nuts
She lived off of White Rice, Rice Crispies, Potato Chips and Soy Milk (Even though she was allergic to soy the doctor said soy milk was much better for her than rice milk). Cereal for breakfast, steamed rice for lunch/dinner and chips for a snack, easy as pie.
If you want to stray from that is gets harder though. We got pretty creative with the recipes too. We made or attempted to make wheat free/vegan: Pancakes, Birthday cake, waffles, muffins, cookies and other baked goods. Paul Newman ("Mah boy says he can eat fitty eggs, he can eat fitty eggs") has a great line of wheat free/vegan cookies too.
So it is possible. I am now an expert on food labels and what milk derivatives can be hiding in products (for instance, manufacturers can put whatever they want into "natural flavoring" without tell you there are milk/animal products in there. Also McDonald's uses milk in their fries, and never told anyone for many years.)