Carrot Cake and Cream Cheese Frosting

It was my youngest son's birthday about a month ago. I usually go to Stater Bros. and get a free birthday cake from the bakery, but when I went this year, they said they only give the cake away if you buy a sheet cake to go with it! What?? Now I have to MAKE a cake for my 1 year old?! I was not pleased.

I decided to make this carrot sheet cake with cream cheese frosting. I mostly like it because the frosting is sooooooooooo good. And I'm not a frosting fan, so that says a lot. This recipe comes from my Cooking Light cookbook.

Cake:
9 T softened butter
2/3 c packed brown sugar
1/2 c sugar
2 eggs
2 egg whites
2 t vanilla
2 c flour
2 t baking soda
1 t cinnamon
1/4 t salt
3/4 c buttermilk
2 c finely shredded carrot

Frosting:
1/2 c neufchatel cheese (just like cream cheese but 1/3 of the fat. It should be right next to the cream cheese at the store)
1/4 c butter softened
2 t vanilla
1/8 t salt
2 3/4 c powdered sugar

Preheat oven to 350. Coat a 9x13 baking pan with cooking spray. Place 9 T butter, brown sugar, and white sugar in a large bowl, beat with a mixer at medium speed for 5 min or until well blended. Add eggs and egg whites, 1 at a time, beating well after each addition until pale and fluffy. Beat in 2 t vanilla. Combine flour, baking soda, cinnamon, and 1/4 t salt, stirring with a whisk. Add flour mixture and buttermilk alternately to the sugar mixture. Stir in carrot and pour into prepared pan. Bake at 350 for 30 min or until a toothpick inserted in the center comes out clean.

For frosting, place cheese, 1/4 c butter, 2 t vanilla and 1/8 t salt in a bowl. Beat at medium speed until smooth. Gradually add 2 c powdered sugar, beating a low speed until smooth. Stir in remaining 3/4 c powdered sugar. Cover and chill 30 min. Spread frosting on top of cake after it has completely cooled and add sprinkles if you want.

Does it count as healthy if there are carrots in it?