It is advisable to read any links posted by others who are attempting to assist with your request.
I posted this link initially in reply#7

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Just for your info....There is no central bdm registry in Australia. Each state and territory has it own registry. Only the State of NSW permits accredited agents to transcribe certificates from its records.
Are you sure that Emma was Robert's daughter?
She married with the surname
LITTLEJOHNS and named her father as Robert
LITTLEJOHNS, Cooper which co-incidentally was Robert
QUARMS's occupation in 1851.
Was Emma illegitimate or was her mother was married previously?
Cheers
Cando