QuickTime itself does not seem to offer this functionality therefore you have to resort to some other means to hide the cursor. On OSX there are some tools that allow this.
Cursourcerer is the first that springs to mind. However, as this really hides the cursor, it might not be ideal as you yourself will not be able to see what you are doing.
However, if you do not need to use QuickTime per se, it seems there are commercial screen recording solutions allowing this sort of thing such as Screenflow. I am not affiliated but the price seems reasonable and there is a demonstration of desired behavior here.