Your result
Australia — Citizenship by Descent
Likely
You were born in Australia before 20 August 1986, which almost certainly means you are an Australian citizen already, by birth rather than by descent. Until that date, being born on Australian soil conferred citizenship regardless of your parents' nationality or immigration status.
So there is nothing to apply for and no eligibility to establish. What you need is proof. An application to the Department of Home Affairs for evidence of Australian citizenship produces a citizenship certificate, and that together with your Australian birth certificate is enough to apply for an Australian passport.
Two things can disturb this, and both are worth ruling out now. If you voluntarily acquired another country's citizenship as an adult before 4 April 2002, you may have lost your Australian citizenship automatically under the law as it then stood, without ever being notified. If that describes you, resumption rather than proof is your route, and it is a straightforward application. The other exception is narrow: children born in Australia to foreign diplomats did not acquire citizenship by birth.