It would obviously depend on one's proximity to the few electric telegraph stations (especially on the New Zealand side), but in theory, only a few minutes. By 1880, the major cities on both main islands of New Zealand were connected to electric telegraphy networks, and there were already links between New Zealand and Australia and Australia and the outside world (including England) by that date as well. The thing that would take the most time would be for the message writer to get the message to the telegraph office, and then for the messenger on the New Zealand end to get the message to the recipient.

Follow-up question: what about in 1800, before the invention of the telegraph?