Preheat the oven to 350 degrees and grease two 6-donut pans.
In a small bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt. Set aside.
In a large bowl, stir together the eggs, pumpkin puree, maple syrup, coconut milk, and coconut oil.
Add the dry ingredients to the wet ingredients, and stir together until combined.
Transfer the batter to the donut pan, smoothing down the batter of each donut with a small spatula.
Bake for 15 to 17 minutes, or until the donuts are set and a toothpick inserted into one of the donuts comes out clean. Cool on a wire rack.
Store the donuts in an airtight container for a few days, or transfer them to the freezer. Makes 12 donuts.