Check out this recipe for Carrot Cake from Dr. Weil.
It has wheat flour, carrots, pineapple, and applesauce instead of a lot of oil and sugar, and is really moist and delicious for the whole family. I topped a sheet cake with a version of cream cheese frosting for the family, and then made my daughter her own small carrot cake topped with a little fresh whipped cream. (I was afraid her little body would go into sugar overload from a ton of sugary cake/frosting as well because she just hadn't had it). Hope this helps!