Preheat oven to 350°F (175°C). Grease and line a 9×5-inch loaf pan with parchment.
Grate zucchini; measure 1½ cups. Toss blueberries with 1 tablespoon flour.
In a large bowl, whisk eggs, oil, granulated sugar, brown sugar, and vanilla.
Add flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Stir until just combined.
Fold in zucchini and floured blueberries.
Pour batter into pan; smooth top.
Bake 55–65 minutes, checking at 50 minutes. Toothpick should come out with a few moist crumbs.
Cool in pan 10 minutes, then lift out and cool completely on a wire rack before slicing.