Preheat oven to 350 degrees. Oil a standard 12-cup muffin tin or line with paper liners. In a bowl, combine sugar, vegetable oil, orange juice, 1/2 teaspoon vanilla extract, and eggs.
Stir in baking powder, baking soda, allspice, and salt. Add flour; mix. Stir in carrots, walnuts, and coconut.
Divide batter evenly among muffin cups. Bake until toothpick inserted in centers comes out clean, 25 minutes. Let cool completely before frosting.
Meanwhile, in a mixing bowl, combine cream cheese, confectioners' sugar, and remaining 1/2 teaspoon vanilla extract. Whisk until smooth.
Frost cupcakes, and garnish with shredded coconut.