It would very hard to accommodate, especially the dairy. That said peanuts/tree nuts are not the only allergen that can cause anaphylaxis or extreme reactions. My DD is severely allergic to peanuts and eggs and the egg is just as dangerous for her as the peanuts. I would feel more comfortable sending her to a carer that was completely allergen free because little kids share everything and it is so hard to monitor. But I do thank the universe dairy isn't an issue for us as that would be so hard to accommodate on top of egg and peanut.

Incidentally in many western cultures egg is a relatively new addition to widespread baking (as in post war) so most old-school recipes don't even have eggs.