Combine dry ingredients (flour, baking powder, salt, cinnamon, nutmeg, allspice) in a large bowl. In a separate medium bowl, mix wet ingredients (eggs, eggnog, sugar, melted butter, vanilla extract, rum extract).
Combine wet and dry mixtures, stir until just combined. Pour batter into greased loaf pans and bake at 350 degrees for 30 minutes (mini loaves) or 50 minutes (large loaf).