Preheat the oven to 350°F Lightly spray an 8 1/2-by 4 1/2-inch loaf pan with vegetable oil.
Mix the oil, eggs, granulated sugar, cinnamon, nutmeg, vanilla and yogurt in a large bowl or food processor until well combined. Stir in the carrot, apple and raisins.
Combine both flours with the baking powder and baking soda in a separate bowl, mixing well. Add to the egg mixture and stir just until combined. Pour the batter into the prepared loaf pan. Sprinkle with the brown sugar and bake in the center of the oven for 35 to 40 minutes, or until a tester inserted in the middle of the loaf comes out clean.
Cool in the pan for 15 minutes, then turn out onto a rack. Serve warm or at room temperature.