The relationship that Australia has with New Zealand is better developed and more extensive than with any other country.
So New Zealanders are able to visit, work and live in Australia indefinitely under SCV.
But with criminal history, should apply for a visa to travel Australia.
http://www.australia.org.nz/wltn/VisaFAQ.html#work
However I just don't like that we still have to carry the passport between two countries and should clear each customs. I think it might be the time to start thinking for Tasmanian Federation?