Preheat oven to 350°F and line a 12-cup muffin tin with cupcake liners.
In a medium bowl, whisk together the gluten-free flour, almond flour, baking powder, baking soda, salt, nutmeg, and cinnamon until well combined.
In a large bowl, cream together the sugar and 1/2 cup softened butter until light and fluffy, about 3 minutes.
Add eggs one at a time to the butter mixture, beating well after each addition, then mix in vanilla extract and rum extract.
Alternate adding the dry ingredients and 3/4 cup eggnog to the wet ingredients, beginning and ending with dry ingredients, mixing gently until just combined.
Divide batter evenly among the cupcake liners, filling each about 2/3 full.
Bake for 20-22 minutes, or until a toothpick inserted in the center comes out clean, then cool completely on a wire rack.
For the frosting, beat together cream cheese and 1/4 cup butter until smooth and creamy.
Gradually add powdered sugar, beating until fluffy, then mix in 3 tablespoons eggnog until you reach desired consistency.
Pipe or spread frosting onto cooled cupcakes and garnish with freshly grated nutmeg before serving.