There are lists for passengers arriving to Sydney, for ships up to 1922, although not everything beyond 1900 has been transcribed yet.
http://mariners.records.nsw.gov.au/
Also many ships arriving to Sydney and Melbourne and Brisbane, which would be the likely ports from NZ, had their passengers listed in the shipping news of the papers, so you could try the Trove Newspaper website.
http://trove.nla.gov.au/newspaper
Diane