How long do you need to live in Australia before you are eligible for the Australian Pension or to be an Australian citizen?
If you hadn't moved to OZ before Feb 2001, you will never be eligible for any social benefits. You can get the pension after you retire. Unless you apply for PR (just like others apply for PR in NZ), you can never become an Australian citizen.
If you want to get any social security payments, you should start applying to be an Australian Citizen as soon as possible. This involves going through the regular visa application process (i.e. applying for a skilled migrant or family visa) and once permanent residence is granted, waiting a further 2 years before being eligible to become an Australian Citizen. Once you are an Australian Citizen there is often a stand down period as well before social security benefits become available to you. I would suggest looking at http://www.immi.gov.au/ to see if there is a suitable Visa for you and then contacting Centrelink to check on the Age Pension requirements http://www.centrelink.gov.au/internet/internet.nsf/payments/age_eligible.htm
All the best :) Grace