Preheat oven to 350°F (180°C) and line a loaf pan with cooking spray or grease.
In a sieve over a large mixing bowl, sift the flour until fine. Add the baking powder, baking soda, cinnamon, nutmeg, allspice, and salt. Combine well.
In a separate bowl, add the white sugar, brown sugar, canola oil, almond milk, apple cider vinegar, and vanilla extract. Use a whisk to combine.
Add the flour and spice mix to the bowl and combine all ingredients well. Gradually fold in the grated zucchini to create an even distribution through the dough.
Carefully pour the dough into the loaf pan. Bake in the oven for 40 minutes, until the top has browned and inside is moist but not wet. Remove from oven and allow to cool for 10 minutes.
Remove bread from loaf pan and slice to serve