Preheat oven to 350 degrees. Grease bottom of bread pan. Beat eggs, add sugar, eggnog, butter, rum, and vanilla. Blend well, add flour, baking powder and nutmeg. Stir until just moistened. Pour into greased pan. Bake at 350 degrees for 45-50 minutes or until toothpick comes out clean. Cool 10 minutes. Remove from pan. Cool bread completely before slicing.