Your result
Australia — Citizenship by Descent
Possible
You were born outside Australia before 26 January 1949, the day Australian citizenship came into existence. Before that date people in Australia were British subjects, so nobody's parent can have been an Australian citizen on the day you were born, and the ordinary descent test cannot apply to you.
The law deals with this separately rather than shutting you out. You may be eligible if a parent of yours became an Australian citizen on 26 January 1949, and that parent was either born in Australia or in the former Territory of New Guinea, or had been naturalised in Australia before you were born. It turns on your parent's exact position on that date, which is why this cannot be called from here.
Claims this old usually stand or fall on documents rather than on the law, so start there. Your parent's birth or naturalisation certificate is the thing to find, and records from that period sit with state and territory registries of births, deaths and marriages and with the National Archives of Australia, not with the Department of Home Affairs.