In a large mixing bowl, toss together the carrots, walnuts, pineapple, raisins, and coconut with 1/2 cup of the flour to coat them and keep them from sinking to the bottom of the cake batter.
Sift together the remaining 1 1/2 cups flour, cinnamon, nutmeg, baking soda, and salt.
In a mixer with a whip attachment, mix the eggs and sugar until light and fluffy (the "ribbon" stage) then drizzle in the vegetable oil. Fold in the dry ingredients and pour over the carrot mixture. Fold carefully to blend, then pour the batter into a buttered, floured 10 by 3-inch cake pan containing a circle of parchment paper in the bottom. Bake until firm to the touch in the center, about 1 to 1 1/4 hours. Let cool on a rack and then turn out. Dust the top with powdered sugar and cut into wedges to serve.