Recipe for Carrot Cake that does NOT use refined sugar or chemical substitutes?

Okay, frosting is sweet, so therefore made with some kind of sweetener. Applesauce is usually used in cakes to replace the oil or er. Cake is called cake because it's sweet. Your child will be just fine if given a little sugar. It's the overuse of sugar that causes problems or eating it to often. Your being to overcautious. Everything in moderation.