Grease and flour two 8x1-1/2-inch or 9x1-1/2-inch round baking pans. Set the pans aside.
In a large mixing bowl, combine the flour, sugar, cinnamon, baking powder, baking soda, salt and allspice. Add carrot, undrained pineapple, mayonnaise and eggs. Beat with an electric mixer on low speed till moistened. Beat on medium speed for 2 minutes, scraping bowl occasionally. By hand, stir in walnuts.
Pour the batter into the prepared pans. Bake in a 350 degree F oven for 30 to 35 minutes or till a toothpick inserted near the centers comes out clean. Cool on wire racks for 10 minutes. Loosen sides. Remove cakes from pans. Cool thoroughly on wire racks.
To assemble, place 1 cake layer on a serving plate. Spread layer with about 1/2 cup of the Cream Cheese Frosting. Top with second layer. Spread top and sides with the remaining frosting. Store, covered, in refrigerator. Makes 14 servings.
In a large mixing bowl, beat cream cheese, butter, and vanilla with an electric mixer on medium speed till light and fluffy. Gradually beat in enough powdered sugar (about 4 cups) to make a frosting of spreading consistency. Makes 3-1/2 cups.