The Verdict: Need More Info
Your claim turns on your parent's position on 26 January 1949, the day Australian citizenship began. Find their birth or naturalisation certificate, which shows whether they qualified.
Nobody was an Australian citizen before that date, so the ordinary descent test cannot apply to you. A separate rule covers you instead.
You may be eligible if a parent became an Australian citizen on 26 January 1949 and was born in Australia or the former Territory of New Guinea, or had been naturalised in Australia before you were born.
Records from that period are held by state and territory registries of births, deaths and marriages and by the National Archives of Australia. With your parent's record in hand, you apply for citizenship by descent to Home Affairs.