Don't deprive your child however.
Substitutes are always available for almost any product.
Easier to find are soy milks and sometime goats milk. Mocha mix non-dairy milk substitute is available at most supermarkets, as well as Mocha mix ice cream. Don't let them overdue this one because of sugar content. Tofurella comes in cheddar, Mozzarella and Jalepeno for the brave. These actually melt and make a reasonable fake pizza or fake grilled cheese sandwich.