there are rabbit rescue centres for rehoming bunnies! http://www.rabbitrehome.org.uk/centres.asp
they do make good pets and some people even keep them as indoor rabbits but they certainly enjoy being able to stretch their legs so a decent sized run is important as well as a hutch in the garden.
Its important to get them used to being handled as the back legs are strong and can give a good kick and scratch if they are not securely held.
important to have yearly vaccinations for Myxymatosis & VHD so vet bills a consideration.
It may be worth considering a guinea pig as a less expensive pet (no vaccines required) and often easier to handle for a child.
hope that helps