The man you want to talk to is John M. Flores (which is his user name here). He has both the Q and mft systems and uses them professionally photographing for a motorcycle travel magazine. If anyone can answer your question, he's definitely a guy that can.
That said: with a child you never know if they'll stay with it. Older micro four third systems are cheap these days and if he does get serious there are more avenues to expand with a huge number of lenses and bodies available.
The problem with the Q is: very few lenses. If you want to really do more with your photography you'll need to buy into a whole new system, but with mft cams you can just buy more lenses or upgrade to a later body and use your existing lenses.
The economics aren't much different since the older micro four thirds bodies are selling for like $100 to $150 dollars these days. Used kit lenses for well under $100.
Lots of good used deals at
Buy & Sell New & Used Cameras – Canon, Nikon, Hasselblad, Leica & More - KEH.com if you want to poke around over there. I've bought several things from them and they are one of the better used camera dealers around.
EDIT: Oh and you said four thirds rather than micro four thirds? They appear to be dying out. Same sensor size, but the DSLR style system of four thirds is not being advanced like the mirrorless micro four thirds systems are. I don't think it's necessarily a great choice long term -- although there are some AMAZING four thirds lenses out there.