Working backwards, just on Rev McIntyre
1. Rev Wm McIntyre was in Sydney, NSW in 1840 See cutting
http://trove.nla.gov.au/ndp/del/article/31725200 The Colonist 1 July 1840 when Rev Wm McIntyre was the minister who conducted the marriage ceremony of Rev James Fullerton and Mary Jenkins.
2. Check NSW BDM online index to see if the FULLERTON marriage has been indexed in the Early Church Records, and notice that it does NOT seem to be indexed.
3. Check the familysearch.org site Records and find the following for that marriage and find that there’s a parish register entry dated 4 July 1840 for that marriage. Likely it is difficult to transcribe as it has Mary’s surname as “Leukins” instead of Jenkins, but note that there’s a parish register… that’s the important fact in this ‘thought line’
https://familysearch.org/ark:/61903/1:1:XTZD-RBS 4. So that is showing that Rev William McINTYRE was in Sydney in June 1840, and recording events in his parish register/s.
5. Here in Sydney 18th May, Rev William McIntyre marries another couple.
http://trove.nla.gov.au/ndp/del/article/31725072 Colonist 23 May 1840. That marriage IS indexed at NSW BDM, it is there as Stephen OWEN ad Rebekah CROOKE . the details can be found in the parish register for “JA ” which of course is Scots Church, Sydney.
http://www.bdm.nsw.gov.au/Pages/family-history/early-church-codes.aspx 6. So, Eliza Hamilton may well have been baptised by Rev William McIntyre, in Sydney in March 1840, as here’s another marriage that he conducted, this time in January 1840...
http://trove.nla.gov.au/ndp/del/article/31727246 Australasian Chronicle 10 January 1840. And that marriage is findable at NSW BDM online, again recorded “JA” , So, it is possible that Eliza was baptised and that the baptism will be in the register for 'JA' PERHAPS mis-transcribed, but likely in the register and in chronological order.
So, civil registration of BDM events does not commence in New South Wales until 1856. Prior to that time, and dating from 1810, the clergy of all denominations were meant to transmit details from their own parish registers initially to the Sydney based NSW Chaplains. By the 1840s this regulation was becoming difficult to enforce, and not all records from that era have survived. Worse still, (from a family history perspective) in the 1840s there was a significant faction that separated from the Church of Scotland, and Rev McIntyre was part of that separated group. So, depending on which register stayed with which organisation, and if the register remained extant to at least become available for filming in the early 20th Century….
Anyway, here’s some info about the Reverend who likely baptised Eliza HAMILTON
http://adb.anu.edu.au/biography/mcintyre-william-4103Penrith NSW
https://en.wikipedia.org/wiki/Penrith,_New_South_Wales Prebysterian Archives contact details noted at the link below:
http://www.nswtranscriptions.com.au/pages/useful-addresses.php(remember of course that Church records are NOT public records, and you need to be patient and wait for volunteers to process any requests)
ADD
Several localities "Mt Pleasant" in New South Wales, all over the place.
It seems that Mt Pleasant near Penrith may be known today as Cranebook. (not to be confused with another Cranebook in NSW)....
https://en.wikipedia.org/wiki/Cranebrook,_New_South_WalesPHOTOS
http://photosau.com/penrith/scripts/home.asp Cheers, JM