Combine water and sugar in a saucepan; cook over low heat 2 minutes or until sugar dissolves.
Remove from heat; stir in rum, lime juice, and rind.
Pour mixture into the freezer can of a 1/2-gallon hand-turned or electric icecream freezer.
Freeze according to manufacturer's instructions.
Arrange kiwifruit and scoops of daiquiri ice on plates; garnish with mint and lime, if desired.