Children can play quidditch! But much like football, the rules must be modified to emphasize safety and accessibility.
usquidditch.org is the best resource for these modifications. Once you familiarize yourself with the standard game of quidditch, please review these links to adjust the game for your target group.
Non-tackling quidditch can make defense exceedingly difficult, so one suggested modification is that chasers on offense may not enter the keeper zone.