You can make egg free icing with icing sugar, cream of tartar and water or milk . Start with 2 cups and 1/4 teaspoon cream of tartar. Cream of tartar is also good for making merangue for pie stiffer..
Hi, in Italy many chef pastry use hyfoama as a substitute for egg white. It's a derivative of milk.
Recipe for royal icing:
icing sugar 2400gr