Preheat your oven to 350°F (175°C). Grease a loaf pan.
In a bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg.
In another bowl, mix sugar, oil, and applesauce. Add eggs and vanilla, and mix well.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the grated zucchini.
Pour the batter into the prepared loaf pan.
Bake for about 60 minutes, or until a toothpick inserted into the center comes out clean.
Let the bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.