I'm finding this really interesting!!
Many years ago, in the 50s-70s you could an 'Extract' of a Birth Entry. The 'Extracts had the person's name, date and place of birth, BUT no parents' details, and were certified by the Registrar. About A6 size - sometimes paper, sometimes card. They were usually used when first enrolling a child at school or similar event.
To get a passport then (which you didn't need for Australia until the late 70s?), you required a 'Full Birth Certificate' - along the lines of what we have today .... name/dob/place of birth/sex/parents names, ages, place of birth/mother's maiden name/father's occupation. The parents also supplied the date and place of marriage which was recorded in the Birth Register but NOT on the 'Certified Copy of Birth' - altho' it would be typed on the back of the certificate if requested!!
I wonder if some churches provided an 'Extract' of the Marriage Entry from their Register?? A shortened version along the lines of the Birth Extracts?? And that's what you have??
Certainly I have copies of my parents' original marriage certificates (1946-1957 = 3 in total), all in churches, and they all have the parents details on them. Maybe a hunt thru' the relevant legislation on a wet, windy day when there's nothing else to do ....
Best wishes
Elli