So you are seeking a baptism for a baby boy born circa 1818 in Oxfordshire, given names of John Benjamin, a son of James Moss Aaron DAVIS and his wife, Hannah nee BROWN …
May I share some thoughts…
Wollongong is around 230 miles from Molong, and there’s several Police Districts between them too.
I am concerned that you have him at Wollongong as Chief Constable from 1851 for many years… I think they went to Molong and were stationed there for many years before returning to Wollongong in the mid 1860s…. I see a marriage at St Michael’s, Wollongong, (CofE) by special license, 18th August, 1852, Rev M.D. MEARS … Mr John DAVIS to Miss Sarah Emily, eldest daughter of Mr William ORGAN, late of H.M. 28TH Regiment Foot.
https://trove.nla.gov.au/newspaper/article/59775198 Bells Life 28 Aug 1852
https://trove.nla.gov.au/newspaper/article/12939425 SMH 23 Aug 1852
https://familysearch.org/ark:/61903/1:1:XTC2-ML8 : 10 February 2018 FHL 993964 (Batch M31026-3)
BUT, but ... after marriage, and birth of Maria Jane, I see John and Sarah Emily well away from Wollongong for many years, perhaps not back residing in Wollongong until mid 1860s … as births to the couple were registered Wollongong district from about 1864…
Maria Jane, born 11 Oct 1852, daughter of John & Sarah Emily DAVIS, of Harbour St, Wollongong, (he as Chief Constable), was baptised December 5, 1852, St Michael’s Wollongong
I see a baby born 10 April 1855, Eliza Best, daughter of John and Sarah Emily DAVIS, baptised Wellington 24 June 1855. (Wellington and Molong Police Districts adjoin each other)
NSW BDM online index has this as Volume 42A, line 1764, of 1855.
https://familysearch.org/ark:/61903/1:1:XTHN-WMN 11 February 2018
993965 / C21026-4
Bathurst Free Press 29 Nov 1862
At the Railway Hotel on Friday 28th November of Croup and Diptheria, Hannah Louisa Organ DAVIS, third daughter of John and Sarah Emily DAVIS, late of Molong.
https://trove.nla.gov.au/newspaper/article/62720694 Also, despite much reading, cross referencing etc ... I have not found John’s middle name of Benjamin recorded anywhere in my offline resources, … sorry, I have a great deal of NSW family history, particularly C of E, but not everything ...
BUT ….. I can see Sarah E, Sarah Emily with John, but just NOT with John B or John Benjamin…
On the other hand …
a birth registered in 1868, in Wollongong District for a William J B, son of John and Sarah E DAVIS, #18219 … likely leads to
NSW ER 1902 ILLAWARRA, polling at Wollongong
William James Belmore DAVIS, Denison St, a carter
And again on that other hand
NOW I MENTION that the electoral rolls, like many other official records from that colonial era, contain spelling errors, often because the information was given verbally, and recorded with best endeavours, but not by people who needed to be excellent spellers, so on same page as William James Belmore DAVIS (NSW ER 1902, ILLAWARRA, polling Wollongong - 1902 was first NSW roll to include females. Ancestry has 1903-4 roll.)
Sarah Emily DAVIES, Denison St, domestic duties
Alfred John DAVIES, Denison St, labourer
Isabel Annie DAVIES, Denison St, domestic duties
Yes, Denison St was and still is a longish street.
OF COURSE, the electoral rolls from that era do not include house numbers or house names, and of course don’t give marital status, so I am simply speculating that perhaps you may be interested in the DAVIES v DAVIS consideration, as there’s a birth for Alfred J A, son of John & Sarah E, DAVIS registered 1871, Wollongong District. #19590.
Good luck with James Moss Aaron DAVIS, that combination of given names should give identifying info for your quest.
JM