From the relevant page dealing with 'eVisitors' (which are effectively electronic tourist visas):
"If you have had any criminal convictions in any country, you may wish to consider applying for a Tourist visa (subclass 676), rather than an eVisitor. If arriving on an eVisitor with criminal convictions, you could be refused entry into Australia".
Source:
http://www.immi.gov.a...sitor/obligations.htm
The Tourist Visa (subclass 676) page states "You must meet certain character requirements":
http://www.immi.gov.a...t/676/eligibility.htm
The First Working Holiday Visa page states "To be granted this visa you must meet character requirements":
http://www.immi.gov.a...eligibility-first.htm
Both of those pages link here:
http://www.immi.gov.a...aracter-requirements/
(Check the links under 'Character-related information' for further details)
Chris