Confirming Harriett Cole's birth 9 May 1833 to Amos and Phaebe COLE
https://familysearch.org/ark:/61903/1:1:XTC8-2S3This would seem to be the birth for Harriet:
735/1833 V1833735 17
Harriett C COLE,
parents: Amos, Phoebe
Judith
Perhaps this may be of interest .... Harriet Cole Percy, maiden name COLE, burial 25 Feb 1898
https://familysearch.org/ark:/61903/1:1:QVGN-RPZRAmos SCOLS ex the Henry of 1823 C of F 19 Feb 1830 was a shoemaker and assigned to Lieutenant REID and/or William COX.
Elizabeth HARRISON ex the Sovereign of 1829 T of L 1834 and allowed to remain in the district of Invermein
Charles, son of Phoebe STIRRUP alias Elizabeth HARRISON, of Birchgrove near Sydney was born 12 February 1831 and baptised 20 March 1831 by Rev William COWPER, and the ceremony was registered in the parish registers at St Philip's C of E, Sydney.
I think you will find the record for Charles baptism at NSW BDM under the following ....
Covenant C STIRRUP, with mother as Phebe Alias Elizabeth HARRISON Volume 1C, line 10394 of 1831 and as Covenant C STIRRUP, mother as Phebe, Volume 15, line 196 of 1831.
http://www.bdm.nsw.gov.au/Pages/family-history/family-history.aspx Here it is as Covenant Charles HARRISON, born 12 Feb 1831, baptised 20 March 1831, with both versions of his mum's name. It was not unusual in those times to find several versions of a person's name. The word "alias" on NSW records does not indicate any illegal practices, nor attempts to hide behind a name. Often, in the NSW records a female may be recorded with several sets of names ... including for example
Her names at birth/baptism
Her names that she became known by in her local community before coming to NSW.
the names recorded from verbal information given in one accent, recorded by a person with a completely different accent, when landing in NSW
the mish-mash of names caused by lack of standard spelling, and lack of literacy of the person recording the verbal information and the lack of literacy of the informant him/her self.
https://familysearch.org/ark:/61903/1:1:XTCD-5QZ In the 1810-1821 era, the NSW governor of the penal colony set out some general orders that gave structure and administration to the colony. Today we spell his names as Lachlan MACQUARIE. Even he varied the spelling of his family name on official documents .... even within the one document, yet without his general orders re recording of baptisms and burials and transmitting those records to NSW Chaplains, we would likely be much less informed family historians.
Cheers, JM