It's not across-the-board illegal for a child to possess a gun in the US, although it varies by state.

Age-based gun restrictions are usually about non-parents selling or giving guns to minors, or carrying in public without adult supervision.

Firearms accidents are not a common cause of death; according to the CDC they amount to about 1% of all accidental deaths of young people.

http://www.cdc.gov/nchs/data/dvs/deaths_2010_release.pdf