Hi Kellie,
You've likely found the 1875 marriage record indexed at
https://bdmhistoricalrecords.dia.govt.nz/search. There's a matching record index at
https://wilsoncollection.co.nz/ that records they were married at Knox Church, Dunedin. At that time many immigrants were arriving at Port Chalmers (Dunedin) and living in Otago or Southland.
The closest thing to an official NZ Immigration passenger list is stored here:
https://www.familysearch.org/search/collection/1609792 . At that time it's not very complete, but there is one "Sarah Kent" recorded as arriving at Otago in 1874 (an unmarried cook from Middlesex).
There are also passenger lists here, which are not complete but not too bad:
https://freepages.rootsweb.com/~ourstuff/genealogy/PassengersPortChalmers.htm Browsing the list for Port Chalmers in Feb 1874 leads us to the ship Carnatic (1874). In the list there is a Sarah Kent, 22, cook from Middlesex.
Now that might not be YOUR Sarah Kent, but it's an example of a workflow to find immigrants. If Sarah was born in NZ, it would likely have been before 1860 and birth records may be a bit sketchy at that time, but it's a reasonable bet she was an immigrant.
You can also search the Wilson Collection (link above) for electoral roll and burial records for Sarah Smith - may take some browsing but look for Otago or South Island records for clues.
I also search
https://collections.archives.govt.nz/web/arena#/ to see if they left a will (or divorced, etc). And search
https://paperspast.natlib.govt.nz/newspapers for a death notice or obituary.
Hope that's a start to find NZers.