There's no kill shelters that you can re-home your family pet to (Lort Smith Animal Hospital in Melb is an example) or they look after your pet while you're unable to. This is much more humane than having your family pet killed because they no longer suit your lifestyle. Give someone else the...
If they have good history try applying for a place that says 'no' to pets and be upfront about the dog but negotiate some kind of condition ie more rent or a pet bond (not sure whether this is legal or not) and the LL may be more willing to take them on.
