Preheat your oven to 350°F (175°C). Grease a loaf pan.
In a mixing bowl, combine flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, whisk together oil, sugar, eggs, and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in the grated carrots and chopped walnuts.
Pour the batter into the prepared loaf pan and smooth the top.
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.