Correct.
I distrust these sort of statistics greatly. No one ever questions the data. Thing is, more children die of drowning each year. Should we outlaw water?
But then, why should logic get in the way of these people's agenda?
The study counted everyone up to age 17 as children. I've haven't seen the data myself, but I would be willing to bet half my savings that at least 50% of the child handgun murders were in the 15-17 year old range. I would also bet that the majority of the shootings were from gang fights.
Looking at the states with the highest averages (MD, LA, IL, CA) I see two things in common.
1. Like others pointed out, they have tough gun laws.
2. They have large urban areas (Chicago, Baltimore, etc) with a history of violent gang crime.