I know 16-year olds with their own rabbitry:roll: (and no not just any backyard breeder) Many of these have had rabbits since they were 8-10 years old (I'm guessing the parents had the main responsibility for some of them).
Its rather induvidual. I got my first bunny at 16, and cared for her all by myself
At 19 I still live with my parents, with three bunnies and a hamster that are all my sole responsibility (and the dog when my parents are away:roll: we've had him since I was 11, yet my mom still takes main responsibility for him), and they're happy with driving me to the vets if an emergency happens, also driving the bunnies to shows and jumping competitions.
If children are to have bunnies the parents should be ready to take the main responsibility. Even if the child claims he or she will care for the rabbits, the parents must ensure the rabbit receives food and water every day and has a nice and clean enviourment.
Far too many kids figure out one day that they want a cute little bunny and regardless on how much they beg on forehand, they get sick after just a few weeks and won't care for the bunny anymore. That's why its not wise to buy a rabbit only as a children's pet, and the parents should be prepeared to take over. If not; the kid should not have a bunny, no matter how much he/she begs.