Wouldn't be possible, by 1860 there were many many British European settlers in the South Island, my ancestors for example. In the North Island there was less Euro settlement, but far more Maori settlement, who, as the Land Wars proved, were not keen at all to allow further settlement.
If you can somehow justify how this Israel would work, given that the Imperial Army spent a decade or so fighting in the N Island and given at this time there isn't an organisation that has had several decades of experience in colonisation, fighting or developing a community (say for example the Jewish Agency and the various armed groups in Palestine prior to Independence)
Incidentally, though, one of our early Prime Ministers, from this period was London Jewish, name of Julius Vogel