I have just come across this conversation and have had a similar experience. I am retired and recently came to Australia with my wife, who is an Australian citizen. I wanted a credit card here in Australia for a couple of reasons. My wife and I travel a lot, and hotels and car hire companies, particularly in the US, often insist on a credit card to hold bookings. In addition, many credit cards in Australia have travel insurance bundled in with them and I wanted one of those cards, even although it comes with a substantial annual fee.
I am lucky to enjoy a reasonably comfortable private pension from one of the largest pension funds in the UK, so I thought, naively, that it would be easy to get a credit card. I was amazed to be rejected by the bank on the basis that they will not take any account of UK pension income. This is a bizarre outcome - my income is readibly verifiable and is more stable and predictable than most people in employment, yet I am regarded by banks as having no income. Sadly the Australian Tax Office don't take this view, and will have no trouble in taking substantial amounts of income tax from my pension!
It looks as though I will never be able to get a credit card in Australia based on my income. Has anyone here had a similar experience and found a resolution?