I built a maple board bow for my daughter (then age 5). I found a layout online and scaled it down using her height compared to mine. I tillered until I was sure she could draw it and resulted about 8 lbs @ 18" (she is tall and scrawny). I made some mistakes (hinge in the upper limb) but at 8 lbs, its performed well and she is happy.
She shot the heck out of her first bow and I built another maple board bow for Christmas this year (she's 6 now) to give her more poundage, a shorter bow, and make it a little "prettier." Girls...
Also, I fletched some 1/4" dowels from the hardware store (plenty good for a kids bow). Also needed to use less strands of B50 in her bow string.