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I'm wondering if she may have been buried at the Devonshire St Cemetery.  Their residence was very close to the cemetery, just in the next street I think.

https://en.wikipedia.org/wiki/Devonshire_Street_Cemetery
The Devonshire Street Cemetery (also known as the Brickfield Cemetery or Sandhills Cemetery) was located between Eddy Avenue and Elizabeth Street, and between Chalmers and Devonshire streets, at Brickfield Hill, in Sydney, Australia. It was consecrated in 1820. By 1860, the cemetery was full, and it was closed in 1867.
Re-interment cemeteries
Cemetery locations in the metropolitan region that took re-interments from Devonshire Street Cemetery include Gore Hill cemetery, St Thomas Cemetery in Crows Nest, Rookwood Cemetery, Waverley Cemetery, Balmain Cemetery, Camperdown General Cemetery, Randwick General Cemetery, Bunnerong Cemetery, Field of Mars Cemetery, South Head General Cemetery and Woronora Memorial Park. Remains were also relocated outside the metropolitan area, including Sandgate Cemetery in Newcastle, New South Wales and Berkeley Pioneer Cemetery in Unanderra, New South Wales.

An index created from a number of previous collections of information, including some remaining original cemetery registers, called the Devonshire Street Cemetery re-interment register and index ("microform" format) was produced by the Library of Australian History, North Sydney, 1999. A copy is held by the State Library of New South Wales. A hardback book version was also produced.

Edit to add:
On looking at the index on-line I didn't see the name "Bateup".
https://mhnsw.au/indexes/cemeteries-and-burials/devonshire-street-cemetery-reinterment-index/?query=bateup&page=1

Nor on this list
https://gutenberg.net.au/Devonshire-street/__devonshire-namelist.html


Judith

Yes, as I said, in the early days all communication from outside Australia was by documents carried by ships.
https://www.nma.gov.au/defining-moments/resources/overland-telegraph
In the early days of the colony of New South Wales, communication with Britain – the place that many settlers considered their homeland – could take years. Ships carrying letters between England and Sydney took up to eight months one way and a reliable mail service was really only available to government officials.
The overland telegraph was completed in 1872 and connected with the newly finished Java-to-Darwin submarine cable.  Australia was now connected to the world. News that had taken months to reach England could now be transmitted within hours.

So you can see why shipping was important administratively as well as for personal correspondence and goods.
Shipping notices sometimes included lists of passengers and goods carried.

Judith

As you have said there is nothing on his military record re the days 6 March 1879 to 16 April 1879, although he was listed as being on HMS Danae from 16 April to 7 July.  Both Wolverine and Danae were Royal Navy ships but both were seconded to the Australia Station (the British, and later Australian, naval command responsible for the waters around the Australian continent)
https://en.wikipedia.org/wiki/HMS_Wolverine_(1863)
Danae was a steam corvette, (not to be confused with a WW1 ship of the same name)
https://trove.nla.gov.au/newspaper/article/199358196

Interestingly, Wolverine had only returned into Sydney from a south seas cruise on July 3, 1879, having left Sydney on March 19, 1879; Benjamin had deserted from HMS Sapphire in January.  Benjamin is supposedly attached to HMS Wolverine from 22 February to  March, during which time, according to the newspaper reports, Wolverine was in the South Pacific. (A bit tricky to return to your ship if it's not there  , however perhaps that's the reason for him to be on the Danae)
https://trove.nla.gov.au/newspaper/article/239285434?searchTerm=wolverine

I suspect that he may have been held in the brig of either the Wolverine or the Danae for the 42 days imprisonment and this not on his record as he was not a serving marine for the days of imprisonment.

All bit convoluted!

Judith
If anyone else is interested his RN records can be accessed through
https://discovery.nationalarchives.gov.uk/details/r/D7775167

This would appear to be his death in the NSW BDM index:

1907 #8725, reg Corowa
John CEDERLAND
Parents: JOHN CHARLOTTE

There is an on-line tree which gives his confirmation? (I think!)
From: Finland, Communion Books, 1670-1917

Name   Jöhan Gustaf Cederlund
Birth Date   27 heinä 1840 (27 Jul. 1840)
Confirmation Place   Tampereen tuomiokirkkoseurakunta, Hämeenlinnan maakunta, Suomi (Finland)
Residence Place   Finska:, Tammerfors Stads Församling, Suomi (Finland)
Relation to Head   Scholaris
Volume Year Range   1838-1889

This tree suggests his birth was in Stockholm, Sweden

Judith