I doubt you can do it without being present in Australia - but look here:
http://www.westpac.com.au/personal-bank ... its/apply/The law requires that persons wishing to open new accounts must provide adequate ID (passport, drivers license etc etc), to reach a minimum number of points. The reason is to avoid money laundering et al.
Once you have established you bona fides at a particular bank(s), many will let you open different accounts online - I have done this a couple of times from Thailand when I am chasing better interest rates for term deposits.
Once you have opened an account(s), you will be required to pay a 10% withholding tax on any interest.
You may also wish to google "australia term deposits non-residents"