Hi Roy,

The newspaper, "Otago Daily Times" , Issue 4362, 11 February 1876, Page 2 (http://paperspast.natlib.govt.nz)
lists a Mr "White" amongst passengers on the ship, "Oxford" which arrived at Port Chalmers, February, 1876.

Besides their marriage, the site https://www.bdmhistoricalrecords.dia.govt.nz/ records the births of 6 children between 1881 and 1891. (Check spelling - Isabella Thomson)

You may have found all this already, given the passage of time, but maybe it is useful.

cheers,
Liz