My daughter was 5 1/2 when I built her first bow. It was a maple pyramid bow that pulled about 8 pounds at 19". I took a design from George's site and scaled it down.
I built her another about 6 months later; roughly 16 pounds at 20". Stamped some flowers into the leather handle wrap and made it shiny. She loved it.
I learned a couple lessons:
1). Add a shelf. The satisfaction of building a bow for my little girl and how much fun she was having was kinda dimmed when I had to pull pieces of fetching out of her hand.
2). She is a girl (and a 5 yr old girl at that); like Bowman said, make it pretty. Doesn't have to have a flawless finish or fancy exotic woods, but girls like pretty colors, ribbons, maybe beads and feathers and such. She would probably like to see her name on it. Check out the stuff Pat B has done with patterned tissue paper backings; that is perfect for a little girl. Order some pink barred turkey feather feather fletchings, too.
3). She is growing like a weed (I'm sure you realize this every time you buy new shoes and pants!). Design for more draw weight at a longer draw than she is at; she'll pull what she can and keep getting stronger. The alternative is to plan to replace her bow at least once a year (which she'll like, too).
4). She will love it even if it doesn't have a perfectly elliptical profile at full draw. Just make sure it's safe.
Hope it helps.
John
Boise