Looking for birthday cake recipes for a little guy with a dairy allergy

My son's first birthday is coming up and he's allergic to milk. I want to make him a cake, but all my searches for dairy-free cake recipes turn up recipes that are also vegan, gluten free, and/or sugar free. We're fine with eggs, flour, and sugar.

I searched my recipe books and found a couple cake recipes that don't call for any dairy, but I don't think they'll work. Carrot cake is sad with no cream cheese icing and I'm not sure about sponge cakes because "springy" is one of the descriptors that comes up on lists of choking hazards.