You can buy butter/marg that is dairy free. My sister is dairy free. You can use rice/almond/soy (I'd check on the soy) milk as an alternative in baking I think? And vegetable oil can replace eggs in cakes etc. I use about a half a table spoon for each egg.

Just check that the dairy free child can have soy. That is the usual alternative for people who are dairy intolerant/allergic. If not, rice milk & almond milk should be an option

Good old vegemite should be ok on sandwiches? Or are there nut traces in vegemite?