You can omit the rum, but it is better with it!
In a heavy-bottomed saucepan bring the milk to a boil over medium-high heat.
Stir in the sugar, rice, butter and salt; reduce heat, cover and simmer stirring occasionally until the mixture has thickened and the rice is tender (about 45 minutes).
Meanwhile in a small bowl sprinkle gelatin over 2 tablespoons cold water; let stand until softened (about 10 minutes) then stir into hot rice mixture followed by the rum and vanilla.
Chill the mixture uncovered until cool but not set (about 1 hour).
In a bowl using an electric mixer on high speed, whip the cream to soft peaks form; fold into the rice mixture.
Divide the pudding between glass bowls.
Chill until set (about 1 hour).
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