Preheat oven to 350°.
To prepare cake, lightly spoon flour into dry measuring cups; level with a knife. Combine flour, sugar, coconut, pecans, baking soda, salt, and cinnamon in a large bowl; stir well with a whisk. Combine oil and eggs; stir well. Stir egg mixture, grated carrot, and pineapple into flour mixture. Spoon batter into a 13 x 9-inch baking pan coated with cooking spray. Bake at 350° for 35 minutes or until a wooden pick inserted in the center comes out clean. Cool completely on a wire rack.
To prepare frosting, combine butter and cream cheese in a large bowl. Beat with a mixer at medium speed until smooth. Beat in powdered sugar and vanilla just until smooth. Spread frosting over top of cake. Garnish each serving with grated carrot, if desired.