Preheat oven to 350°F. Spray a 10-cup bundt pan with cooking spray, set aside.
Combine flours, xanthan gum, baking soda, cinnamon, salt, and ginger together in a bowl. Set aside.
In a large mixer bowl beat together eggs, sugars, oil, yogurt and vanilla. Add flour mixture slowly until just blended. With a large spatula, stir in carrots, pineapple, coconut, and nuts. Pour batter into prepared pan.
Bake 45-50 minutes or until toothpick inserted in center of cake comes out clean. Cool on wire rack. Remove cake from pan.
Frosting
Combine 1/3 cup cream cheese, powdered sugar, milk and vanilla; beat until smooth. Frost cake when completely cooled.