Preheat the oven to 350°F. In a medium bowl, whisk together the banana puree, eggs, sugar, olive oil, and vanilla extract.
In a large bowl, whisk together the quinoa flour, superfine brown rice flour, almond flour, tapioca starch, salt, baking soda, and ground cinnamon.
Add the wet ingredients to the dry and mix until incorporated. Fold in the pecans and carrots. Pour the batter into a greased loaf pan or muffin cups. Bake for 45 to 55 minutes for the loaf pan or 15 minutes for the muffins. To check doneness, insert a wooden skewer in the middle, and if it comes out clean, they are done. Let cool in the pan for 20 minutes and then invert onto a cooling rack. Cool completely before slicing the loaf.