Do you have an old Windows laptop lying around that you refuse to touch because of how slow it runs Windows (Vista/7) today? If so, a new product called Neverware CloudReady may be able to help. CloudReady is FREE for Home use.
Neverware’s CloudReady will help you repurpose that laptop into a Chromebook that your young child can use. They have a list of models below that are certified to run CloudReady without any issues here: http://go.neverware.com/
The Verge has a great article below on how Neverware is helping resuscitate these old PCs for schools and other educational institutions.
Have you tried CloudReady already? If so, chime in with your comments and experience. I am planning on trying it out soon myself!