Preheat your oven to 350°F (175°C). Grease a 9x5 inch loaf pan.
In a large bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
In another bowl, beat the eggs, then add the sugar, oil, and vanilla extract. Mix well.
Stir the grated zucchini into the wet ingredients.
Add the wet ingredients to the dry ingredients and stir until just combined. Do not overmix.
Pour the batter into the prepared loaf pan.
Bake for 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.