Yeah, I wouldn't put a kid that age on any kind of strict training regime (in any sport) for physical and psychological reasons (the current 12yo junior national champ here does not formally train, but she sure kicks butt), but letting her do as much as she wants to shouldn't hurt her. There are younger kids who ride 100 mile charity rides out here and a juniors 10-12 racing category. Cycling should be fairly benign since it isn't an impact sport - really it's probably less hard on a kid's body than soccer or gymnastics....
For racing in the states there are gear restrictions, to encourage developing a good spin and so that kids don't hurt their still growing muscles and joints, but that's about all the precaution that the racing community feels need to be made.
There is only one gear for all 18 and under racers who are racing in road races. That ratio is 7.93 meters (26’). That would be equivalent to a 52x14. 52x14 is only an example, the distance at roll out is what's important. There are no gear restrictions for cyclo-cross racing though.
If you are racing track your gear restriction is as follows (this table is taken from USA Cycling ):
17-18: Unrestricted
15-16: 6.78 meters (22'3") (48x15)
13-14: 6.36 meters (20'10.5") (48x16)
10-12: 6.00 meters (19’8”) (48x17)
Why Are There Gear Restrictions?
There are several reasons for gear restrictions for junior racers. The most important may be to avoid injury. Pulled muscles or ligament can be caused when a young person works too hard too fast. Their muscles are not yet fully developed and a pulled muscle can take him or her out of racing for weeks, or more.
Learning to race with good cadence will teach the junior racer and his or her muscles to race better. A higher cadence makes it easier to accelerate. Junior racers need to become comfortable with racing at a higher cadence before they move on to other gear ratios. It is better for their muscle development and will make competition easier later.