An obit to the Dean of Goulburn in 1875 mentions that his church was St Saviour's in Goulburn
http://nla.gov.au/nla.news-article63106159
This may help with the search for parish records which I believe are sorted by church.
I have also had success obtaining transcripts of parish marriages by contacting the NSW state library http://www.sl.nsw.gov.au/research-and-collections/ask-librarian. So if for any reason the National Library doesn't answer your question then you can try the NSW state library (they require the church name). No cost.
Ros

My reply #4, offered a solution to likely elusive blanks on the 1874 marriage at Goulburn NSW. Quite a number of of RChatters, including regulars have used this method to find the info that fills in those blanks. I have received many PMs about these positive outcomes.

Sharon’s # 5 noted she does not have a copy of the registration, and I read it to indicate that the denomination was not confirmed, only that it was by the Dean... It has not ever been a requirement in NSW for any couple’s marriage to be celebrated within a Church building, in fact there has not ever been legislation making any denomination ‘The Established Church’ so the Dean of Goulburn to me indicated that 1874 marriage be Anglican or Roman Catholic. I have a good understanding of Anglican admin practices of that era, and I am scant on Roman Catholic marriages, but in either case, I knew both Anglicans and Roman Catholics Dioceses allowed for the position of Dean.
I continue to be quite sure that the parish register for the 1874 marriage will have much more info, including the information the groom gave to the clergy about himself and his parents, first hand information.

My reply #6, gives several live links including you can easily drill down to an Index to the parish registers of St. Saviour's Cathedral Goulburn 1838-1919 ie the Anglican one and the information that the film is at the Goulburn Municipal Library,

While still at #6 you will notice I provided a live link to this particular pdf
http://catalogue.sag.org.au/attachments/42962/Reel%200176.pdf if you click on that link, You will notice at the top of the first page it reads:
JOINT COPY PROJECT
Society of Australian Genealogists – Sydney
National Library of Australia - Canberra
Mitchell Library – Sydney
To me that indicated there’s a choice of at least four bodies to contact for a lookup request for that 1874 marriage at Goulburn. (Goulburn Library; SAG Sydney; NLA Canberra; NSW State Library, Sydney).

I then checked our OP’s profile and noticed that Sharon is in Western Australia. As the Goulburn Municipal Library is funded at least in part by its ratepayers, and the Mitchell (ie NSW State Library) by the taxes, fees, charges, duties etc charged by the NSW Government and SAG by its annual membership fees, I choose to suggest our OP contacts the National Library in Canberra as it is funded from the federal government, ie from contributions from each of the states and territories including of course our OP’s state of W.A.
ADD
https://sds.asn.au/family-historians http://archival.sl.nsw.gov.au/Details/archive/110326192JM