Preheat the oven to 350 degrees F. Grease the bottom and ½ inch up the sides of a 9 x 5 x 3 inch loaf pan.
In a large bowl, whisk together the flour, baking powder, salt, and nutmeg. Make a well in the center of the flour mixture and set aside.
In a medium bowl, whisk together the eggs, sugar, eggnog, melted butter, vanilla, and rum extract (if using). Add egg mixture to the flour mixture and whisk together just until moistened (batter will be lumpy).
Spoon the batter into the prepared pan. Bake for about 45 to 50 minutes. Insert a toothpick into the center of the loaf to check if it's done - it should come out clean. Cool in the pan on a wire rack for 10 minutes. Remove from pan and cool completely on a rack.
GLAZE
In a small bowl, whisk together the sugar, vanilla, and nutmeg. Whisk in enough eggnog to reach a drizzling consistency. Drizzle the cooled loaf with icing. Grate a little bit of fresh nutmeg over the icing, then let the icing set completely before serving or wrapping the loaf for storage.