The full aircraft registrations are ZK-OXF and ZK-OJD. ZK- is the prefix for New Zealand, and note that the designator isn’t immediately obvious eg VH- for Australia, HS- for Thailand.

You may already monitor such sites that provide live aircraft feeds, which can be useful to see the rego and exact type of an upcoming flight (and make that important seat change )

https://www.flightradar24.com/-37.08,174.65/6