1 cup milk
1 (7 ounce) jar marshmallow cream (such as Marshmallow Fluff®)
1/2 teaspoon vanilla extract
1/4 cup rum
1 (8 ounce) container frozen whipped topping (such as Cool Whip®), thawed
Combine milk, marshmallow cream, and vanilla extract in a large bowl; beat with an electric mixer until smooth. Beat in eggs one at a time; mix in rum. Fold in whipped topping with a spatula.
Chill eggnog until serving.