Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the grated zucchini and carrot.
Add the gluten-free flour, baking soda, baking powder, cinnamon, and salt. Mix well.
In another bowl, whisk together the sugar, vegetable oil, beaten eggs, and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Pour the batter into a greased loaf pan.
Bake for 45 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.