The only serious youth bow I found that looks suitable for someone so young is the Tom Thumb thats put out by Stacey Archery.
www.staceyarchery.com/tom-thumb.html
Comes in right or left handed with drawlengths as little as 15" and draw weights as little as 10 lbs. It even has a machined aluminum riser. **** the thing is better than the 20 year old Hoyt bow that I'm currently shooting. Oh Yeah, the price is pretty steep (for a 4 year old) at $179. Whats interesting about it is that as the kid grows you can send the bow back and for $35 they'll change limbs and wheels. It will go all the way upto 25" and 40lbs