Preheat oven to 350°. Combine first 5 ingredients in a large bowl; make a well in center of mixture. Whisk together pineapple and next 4 ingredients; add pineapple mixture to flour mixture, stirring just until dry ingredients are moistened. Fold in carrots. Pour batter into 2 (8-inch) round cake pans coated with cooking spray.
Bake at 350° for 22 to 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on a wire rack 10 minutes. Remove from pans to a wire rack; cool completely (about 1 hour).
Beat first 3 ingredients at medium speed with an electric mixer until smooth. Gradually add powdered sugar to butter mixture; beat at low speed just until blended. (Do not overbeat.) Beat in up to 2 tsp. milk for desired consistency. Place 1 cake layer on a serving plate; spread with 2/3 cup frosting, and top with remaining cake layer. Spread remaining frosting over top and sides of cake.