Hi Christopher,
Two years have passed since I posted my request so I was most delighted to get some feedback.
Cecily has proved quite elusive, but I have confirmed that she was on the ship "Hooghly" which arrived in Pt Adelaide, Sth Australia from Plymouth in 1855. She was on the Single Women's list as Cicely Connor, and if her birthdate of c.1831 is correct she would have been about 24yrs of age. Peter is named as her father when she married in Australia. She married in the Catholic Church and was buried in a Catholic Cemetery in 1903 aged 73yrs.
I was given the Christening details of a Caecilia CONNOR Christened 29.10.1830 Athlone and Drum, Roscommon, Ireland, RC. Father was Joannis Connor and mother Mariae Dolan. As you can see, quite different fathers names but who knows - the rest of the details fit nicely.
Cicely had 5 sons born in Australia, the firstborn named Peter (not a name from her husband's side of the family). 3 of the sons had daughters, the first born all named Mary.
As you said, most of the early civil records in Australia are also hard to find. Not many of the Catholic births in my family were registered but have found some Christening records through the Catholic Church.
Thanks again for contacting me, it was a nice surprise - regards, Sashar