Line an 8-inch square pan with parchment paper and let hang over the side.
In a heavy saucepan, combine sugar, butter, and eggnog over medium heat. Bring to a rolling boil, stirring constantly. Boil for 8 to 10 minutes, until a candy thermometer reaches 234 degrees, stirring constantly. Remove from heat.
Quickly stir in chopped white chocolate and nutmeg until chocolate is melted and smooth. Stir in marshmallow creme and rum extract. Beat until blended and then pour into prepared pan.
Sprinkle a little freshly ground nutmeg on top. Let stand at room temperature until cooled, and then refrigerate overnight until firm.
When completely cooled, cut into squares. Store in a covered container in the refrigerator.