Preheat oven to 350 degrees. Grease bottom only of a 9×5-inch loaf pan, or three 3×5-inch loaf pans.
Blend together the eggs, eggnog, rum extract, sugar, vanilla and butter.
Sift together the flour, baking powder, salt and nutmeg. Add to eggnog mixture and stir just enough to moisten; pour into prepared pan or pans.
Bake large loaf for 40 to 60 minutes, or until a tester inserted in the center comes out clean. Breads baked in the smaller pans require 35 to 40 minutes. Cool for 10 minutes, and remove from pan. Cool completely, wrap tightly in plastic wrap or foil, and store in refrigerator.