Just be aware the Genesis has no let of; I've started a couple of kids off on a RangerIII - it has an amazing range 15-45lbs and 17-28". It can take them a long ways until they need another bow. The Diamond Atomic is another good choice and covers an even lower end; it will go down under 10# and a 12 or 14" draw, the top end is just lower.
Bear Grizzly, Easton XX75 Legacy
Black & Pink package for the Princess: Martin Mystic, Sword Apex, Limb Driver