have you thought about breed atall ?
have a look round any local rescues that have foster homes instead of kennels that way you can sometimes find dogs which are currently fostered with kids / cats / small furries.
http://www.wiccaweys.co.uk for BC’s (and yes – some will live with pet rabbits – I know one who does !!)
there are loads of other places though, the only other one i know is a lurcher one and that might be asking a little much 😉