It's a funny one, society is happy for kids to run, jump, skip, ride bikes, play tag, play sport, do athletics, gymnastics, etc etc, but when it comes to weight training there is a knee jerk reaction. Personally I'd go with what TTT and Silverback have said, it's fine as long as they are supervised and taught the correct way from the start.
Test-E, I believe TTT is correct, I can't be arsed looking for the study, but I'm sure I've seen it before.
In my opinion and what I'll be encouraging my kids to do is start off with gymnastics from a young age, learn about body control, strength and flexibility, I'd also be happy for them to incorporate some BJJ if they were interested. As an early teen or when they are interested in doing some weight training I'd get them involved in Olympic Lifting. I'll be doing my best to keep my kids out of a regular gym