Hi Bob,
There are very few rentals that accept pets because of the general damage that they can do (and I speak as a landlord although not in Sydney). Some people on these threads have suggested offering an increased bond since that would cover any damages and put the landlords mind at rest.
Having said that I know some people have found rentals with pets although again I don't think that was in Sydney.
We're in SE South Australia and around here most dogs are working dogs although there are a few pets too, but we are in regional area.
Have you tried looking through online papers like the
Sydney Morning Herald - Business News, World News & Breaking News in Australia for any articles?
Regards,
Karen