The answer is "it depends on the child." 

My name is Sam Chupp and I am a kids' RPG advocate. I have a mailing list called kids-rpg on Yahoo Groups where we talk about just such issues. There are some resources I'd like to point you to:

http://dragonkin.bearsgrove.com is my podcast - of interest is Episode 2 where you can hear an interview with two younger girls, both of whom started roleplaying before they were 7.

In addition, there is a really nice website called "The Young Person's Adventure League" and it has a lot more information for you. 

http://www.theescapist.com/ypal/ 

 and the email list is 

 kids-rpg@yahoogroups.com

I hope that these resources can help you. If I can be of help in any other way, please don't hesitate to ask.