In large bowl, combine gelatin and brown sugar; stir in boiling water until gelatin is dissolved.
Stir in ice water and rum; refrigerate until chilled and thickened enough to mound when dropped from spoon.
Beat at medium speed until light and fluffy; gradually beat in eggnog in thin steady stream.
Rinse 4 cup (1 L) pudding mould with cold water but do not dry; pour in eggnog mixture.
Cover with plastic wrap and refrigerate until firm, about 4 hours, or overnight.
Invert onto serving plate; cover mould with hot damp tea towel and shake gently until pudding is released.
Garnish with whipped cream.