To a saucepan over medium-high heat, add the water and the sugar. Stir until the mixture heats up and the sugar dissolves, about 2-3 minutes. Remove from heat. Measure 1 cup of the mixture, also known as simple syrup (save any remaining for another use or discard). To the 1 cup of simple syrup whisk in the vanilla, followed by the rum extract and nutmeg. Allow the mixture to cool 5-10 minutes and then add it to the 2c of half and half. Stir well.
Keep in a sealed container (I use a Mason jar) in the refrigerator. Use as you would store-bought coffee creamer. Shake or stir before each use as the nutmeg will settle to the bottom.