In a large mixing bowl, stir together flour, baking powder, baking soda, cinnamon, nutmeg, and salt. In a separate bowl, beat together egg, sugars, applesauce, oil, and vanilla extract. Pour the mixture into the dry ingredients, mixing just enough to moisten. Fold in carrots, raisins, and pecans, then spoon the batter into the loaf pan. Bake for 50-60 minutes, or until the bread is golden brown and a toothpick inserted into the center comes out clean. Cool on a wire rack for 15 minutes before remove the loaf from the pan.