In total agreement with thirteen, it's a great sport for youngsters to become involved with. Being only 9, your son/daughter will not be allowed to compete until the age of 11. However, there'll be plenty to maintain their interest and 9 is a pretty much perfect age to start at.
Depending on how many kids attend the gym you go to, you might get the feeling that initially your child is being ignored to some extent. This is only the case insofar as a coach has to be sure that a newcomer is going to keep coming before they are able to spend too much time with them, so don't take this perceived ignorance as personal, it really isn't.
For the first few months you should get a varied regime, but with an emphasis on technical development. If you son/daughter does spar during this initial period, it will be carefully controlled and he/she should not take any shots; it's all about learning. Shadow boxing, footwork drills, skipping, bag work and exercises are all staples of all boxers and as a general rule, the quality of coaching worldwide in the amateurs is very good. The focus of everyone involved in the sport is the safety and well-being of the boxer - everything else is secondary (the same definitely cannot be said about the pro game!)
Good luck and I hope that the little guy enjoys the sport (I can sympathise as I've tried a few things with my 8 year old and the fact that Dad's a boxing coach has had no effect! We have found rock climbing though, goes to show that there's something out there for everyone.)