Hi there,
Have you searched for your chap via the digitised newspapers site? It is a real Treasure Trove
http://trove.nla.gov.au/ndp/del/home Do you know the names of his parents? This information is often found on NSW passenger lists especially if the passengers arrived as Assisted Passengers via Emigration Schemes of the middle to late 19thC ?
http://srwww.records.nsw.gov.au/indexsearch/keyname.aspx Use this option to search via surname and then if you spot a possible arrival, make a note of the name of the ship and the year of arrival and then search on this link for images of the passenger list:
http://www.records.nsw.gov.au/state-archives/guides-and-finding-aids/nrs-lists/nrs-5316Another website to try :
http://mariners.records.nsw.gov.au/ Why am I suggesting those links? Well, on death certs in several of the Australian States, the length of time in the colonies is noted.
NSW death certs contain a great deal of information, as they come in three parts .... There's the section that contains the family history info, and of course that is often confusing as the informant is often a grieving family member, relying on their own recollections of names of parents of the deceased, marriage/s, spouse names, children's names and ages and quite a deal more. Then there's the section from the medico, giving the cause of death, duration of illness etc. Then there's the section from the funeral director giving the interment info, clergy/denomination, cemetery etc (burial or cremation). So, that info is often helpful in leading to any headstone inscriptions etc.
Before you consider purchasing a NSW BDM death cert, may I suggest you consider the cheaper alternative? I am suggesting that you consider an Official Transcription from one of the several official transcription agents appointed by NSW BDM.
Here's the RChat link to help explain
http://www.rootschat.com/forum/index.php/topic,300394.0.htmlPS, the NSW BDM online index shows the BDM district where the death was registered. That is not always the same as the actual place of death. Hay District includes the township of Hay, but also includes quite a large area in that general location

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Cheers, JM