The University of Sydney hosts the [Australian Stuttering Research Centre](http://sydney.edu.au/health-sciences/asrc/index.shtml). Check out their website or drop them an email. They are likely to have information about groups that are meeting. I don't know how active the [Australian Speak Easy Association](http://www.speakeasy.org.au/) is because their website appears somewhat out of date. You could also get in touch with your local health service (allied health) - speech pathologists sometimes facilitate groups or at the very least would use their contacts to help you find one.