I sent my dog (cocker spaniel) from London to Sydney for GBP 965, with PetAir (
www.petairuk.com), which was the cheapest quote by far. The crate seemed to be a good size and my dog arrived in good condition.
Having a dog certainly restricts the rental options. You can forget rentinga flat (not that you'd want to with a dog...), and I found that about two thirds of rental houses wouldn't accept dogs.
If a landlord does accept dogs, they will generally require the property to be professionally cleaned or disinfected at the end of the tenancy. I've yet to find out whether hiring a steam carpet cleaner and buying a few "bug bombs" will be sufficient to get my bond back!
John.