Preheat the oven to 375 degrees. Grease the donut pan with cooking spray or butter.
In a large bowl, mix together the flour, baking powder, and salt. Mix well and set aside.
In a medium bowl, mix together the eggnog, egg, sugar, vanilla, coconut oil, cinnamon, and nutmeg. Mix well until all the ingredients are combined.
Pour the wet ingredients into the bowl with the flour, baking powder, and salt. Mix well to combine.
Pour the batter into a gallon sized Ziploc bag. Cut off the corner of the bag and pipe the batter into the donut pans.
Bake for 15-20 minutes until a toothpick is inserted and comes out clean. Take the donuts out of the pan and place them on a wire rack to cool.
While the donuts are cooling, mix together the powdered sugar and eggnog. If the glaze is too thin for your liking, add more powdered sugar, a tablespoon at a time until you reach your desired consistency. If the glaze is too thick, add a splash more eggnog to thin it out.
When the donuts are cooled, dip them into the eggnog glaze and serve!