Preheat your oven to 350°F. Lightly grease your baking dish.
In a small bowl, whisk together flour, baking powder, cinnamon, allspice, and salt.
In a medium bowl, whisk together sugar, vegetable oil, and egg until well combined. Stir in flour mixture and use a rubber spatula to fold in grated carrots. Transfer batter to prepared baking dish.
Bake for 25 to 30 minutes, until a toothpick inserted into the center of the cake comes out clean. Place cake (in pan) on a cooling rack, and cool completely before frosting, about 45 minutes.