Preheat oven to 350 degrees. Spray a 9x5 inch loaf pan with non-stick spray and then line it with parchment paper.
In a large bowl, whisk together the gluten free flour, xanthan gum, baking powder, baking soda, salt, nutmeg, and sugar. Set aside.
In a medium bowl, whisk together the eggs, eggnog, oil, vinegar, and vanilla extract.
Pour the wet ingredients into the dry ingredients and mix until just combined.
Transfer the batter to the prepared baking pan and bake at 350 degrees for 50-55 minutes or until a cake tester comes out clean.
Cool completely on a wire rack before icing.
To make the icing, add the powdered sugar, butter, 1 tablespoon eggnog, vanilla extract, rum extract, and a pinch of salt to a large bowl.
Use an electric hand mixer to mix until smooth and creamy. Add an extra tablespoon of eggnog to thin if the icing is too thick. Spread over the cooled bread and top with freshly grated nutmeg or a very small sprinkle of ground nutmeg (optional).
Notes
I use my Nightshade-Free Gluten Free Flour Blend in this recipe. If your flour blend contains xanthan gum, omit what I called for in the recipe.
Use ¼ teaspoon nutmeg for a subtle hint of nutmeg. Use ½ teaspoon for a more pronounced nutmeg flavor.
If your loaf starts to brown too much in the last 10 minutes, loosely cover the baking pan with aluminum foil.