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.
*I almost always prefer freshly grated nutmeg, but in this case, I prefer ground nutmeg. If you would prefer to use freshly grated nutmeg, be sure and reduce the amount at least by half, as fresh nutmeg is stronger than ground.
You can always adjust homemade creamer to your preference. If you like your creamer less sweet, add more half and half until your perfect blend is reached. Or if you prefer it sweeter, add less half and half.