Preheat oven to 350°F. Coat a 9x9x2-inch baking pan with nonstick cooking spray; set aside. In a medium bowl stir together flour, baking soda, salt, baking powder, cinnamon and nutmeg; set aside.
In a large mixing bowl whisk eggs until combined and light. Add sugar and whisk until combined. Whisk in oil and vanilla until combined. Stir in zucchini. Stir in flour mixture. Transfer batter to prepared pan. Bake for 25 minutes or until golden and a toothpick inserted near center comes out clean. Cool in pan on a wire rack.