Residency for immigration/visa purposes has absolutely nothing to do with residency for tax purposes.
If you satisfy the ATO's definition of residency (which is unrelated to DIAC's definition), and you meet the "no house or spouse/dependent"* rule in Canada, as long as you tell the CRA that you are no longer a Canadian tax resident (by filing a departure tax return), you have no tax commitments to Canada.
(there are certain situations where the above may not be true, but that is the general principle that the CRA follows. In general, you can't be a tax resident of two countries (especially when the two countries have a tax treaty (as Canada and
Australia do) at the same time).
(CharR, it is conceivable that you never had to file Canadian tax returns at all while you were here in Oz if you meet the "no house or spouse/dependent" rule)
*No House or spouse/dependent rule: You don't own a residential property in Canada, or if you do, you cannot easily move back into it (i.e. it's rented out at arms-length, and not to a relative or left vacant), and you don't have a spouse or any dependent children living in Canada.