Mary and the four children arrived in Auckland, New Zealand on 25 June 1885 on the Aorangi. The passenger manifest is available for free on FamilySearch, you just need to register to be able to view it. I searched for Mary, but she and the four children are listed togther in the manifest if you view the attached image.
There is no obvious match for William Hunt Gilbertson in the passenger manifests, but the death of a William Hunt Gilbertson in 1924 at the age of 90 is recorded on the New Zealand Births, Deaths & Marriages Online website, so it looks as though he may have travelled separately from the rest of the family, presumably in advance of their arrival in June 1885.
Event Type: Immigration
Event Date: 25 Jun 1885
Event Place: Westland, Auckland, North Island, New Zealand
Event Place (Original): Auckland, Wellington, Canterbury, Otago, Westland, Taranaki, Hawkes Bay, Nelson and Invercargill, New Zealand
Name: Mary Gilbertson
Gender: Female
Age: 48
Birth Year (Estimated): 1837
Departure Date: 1885
Nationality: Yorkshire
Record Number: 23
Ship Name: Aorangi
Reference ID: No
Digital Folder Number: 004412741
GS Film Number: 4412741
Image Number: 00005
Indexing Project (Batch) Number: P00650-5
Citing this Record
"New Zealand, Archives New Zealand, Passenger Lists, 1839-1973," database with images, FamilySearch (
https://www.familysearch.org/ark:/61903/1:1:FS18-H2K : 16 January 2021), Mary Gilbertson, 25 Jun 1885; citing ship , Archives New Zealand, Wellington; FHL microfilm 004412741.