Preheat your oven to 350°F (175°C). Grease and flour a baking pan.
In a mixing bowl, combine the gluten-free flour, sugar, baking powder, baking soda, cinnamon, and salt.
In another bowl, beat the eggs and then add the vegetable oil and vanilla extract. Mix well.
Gradually add the wet ingredients to the dry ingredients, mixing until just combined.
Fold in the grated carrots.
Pour the batter into the prepared baking pan.
Bake for 40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely.