Historically made with brandy or sherry, due to heavy taxes on those liquors in the colonies in the 18th century, rum was deemed an acceptable substitute. After the Revolutionary War, supply of rum declined and Americans turned to domestic whiskey and finally, bourbon as the spirit of choice.
From Jerry Thomas (1862)
Egg Nogg is a beverage of American origin, but it has a popularity that is cosmopolitan. At the South it is almost indispensable at Christmas time, and at the North it is a favorite at all seasons.
In Scotland they call Egg Nogg, auld man's milk.