Using a computer without having a mouse is a difficult task. If you're looking for a mouse for your child, this one could work very well.
From Amazon
Kensington (K72363WW) Wireless Trackball - Orbit Fusion Trackball Mouse with Scroll Ring; Ergonomic Computer Mouse for Right Handed Users, Ideal for Small Desk & Home Office,Black
Compadvance
KENSINGTON Orbit Fusion Wireless Trackball