I found the passenger list for the "Timaru" which arrived in Otago in October 1879. However I don't know how to add this list. Does someone know.
Passenger list in Papers Past:
https://paperspast.natlib.govt.nz/newspapers/OW18791011.2.24.4?end_date=31-12-1879&items_per_page=10&query=barbara+anderson&snippet=true&sort_by=byDA&start_date=28-06-1879