Cook carrot in boiling water 15 minutes or until tender; drain. Place carrot in a food processor; process until smooth.
Lightly spoon flour into dry measuring cups; level with a knife. Combine whole wheat flour and the next 6 ingredients (through cloves) in a large bowl. Combine carrot, sugar, and the next 4 ingredients (through egg white) in a small bowl, stirring with a whisk. Add carrot mixture to flour mixture, stirring just until combined.
Pour batter into an 8-inch loaf pan coated with cooking spray. Bake at 350° for 50 minutes or until a wooden pick inserted in center comes out clean. Cool bread in pan 10 minutes on a wire rack; remove from pan. Cool completely on a wire rack. Cut bread into 12 slices.
Not a sweet, dense sort of quick bread, but a light, almost "sandy" texture. Added chopped walnuts and a good handful of mixed dried fruit. Might sub melted butter for oil next time (more flavor). I made the spice measurements heaping and was glad I did. A bit crumbly, but great with orange or peach marmalade.