I learned the bowyer's trade a few years ago out of a keen interest to put serviceable, realistic, and inexpensive wooden longbows into the hands of medieval reenactors. In the pic below, I'm shooting a 40 lb. draw target longbow, made from a red oak "stave" that cost me all of eight bucks at Lowe's Hardware (no joke). A lot of bowyers, and books about bowmaking, get pretty hi-tech and confusing, but the principles, tools, and skills involved are honestly fairly simple. In one two day bowmaking seminar that I taught, the folks in attendance, all first timers, cranked out thirteen very decent longbows, and far as I know are still shooting them. One very good and helpful source, that I highly recommend is Rudder Bows. Here's a link to their bowmaking stuff
http://216.119.68.89/store/index.php?main_page=index&cPath=6&zenid=0afab8bfec7914aa011a500216ea6781
Jim Boswell is good people, and he's a bowyer's bowyer.
Wish I had time to walk you through making a kid's bow, I've made tons of 'em for the youth archery division. For staves I use carefully selected red oak boards from Lowe's, that measure 2" wide by 1/2" thick by 48" long, and sell for $3.32. I even developed a specially designed arrow rest that prevents the arrow from pulling away from the bow under draw, so I can break kids of that irritating habit (to me at least) of wrapping a finger over the top of the arrow to hold it to the bow.
Can you make your kid a bow? You bet you can. Low draw weight, non-recurve bows are very quick and easy to make. I strongly caution you though on the following point. A kid's bow is short and geared toward a short draw length. If you let any non-bowyer/educated archer adult handle it and try to shoot it, he or she will invariably overdraw the bow and damage it. If you custom make a bow for a little person, he or she is the only one to handle it and shoot it, savvy? Good luck and git 'r done, I guarantee you'll have a blast.
Sarge