Air New Zealand  -  Flight cancellation without any communication

I booked a flight on Air New Zealand from Auckland to Darwin (via Melbourne) - Booking Reference S2APSH.
When we arrived in Melbourne at 5:30PM, we were told that the last leg of our journey (NZ7838) to DWN was no longer operating. I phoned the Air New Zealand Service Desk, but due to high caller demand (60 min wait) we could not get through. I considered booking into a hotel in Melbourne for the night, but realised that due to the Victoria lockdown, it would have resulted in a 2 week mandatory quarantine period for us the moment we arrive in Darwin. I therefore had no option, but to book a flight with Jetstar, at a cost of AUD1830 for both me and my wife.
I contacted Air NZ through WhatsApp who offered me a refund of $450 ($225 per person) for the cancelled flight.
I am instead seeking a reimbursement of $1830 (The cost of my Jetstar flight.)
My reasoning behind this is, that I had incurred these extra costs due to Air New Zealand not informing me about the cancellation prior to my departure from Auckland Airport. Had I known, I would not have travelled to Melbourne.
Key points from the WhatsApp communication:
- Air NZ agreed that they did not contact me to tell me about the
cancellation.
- They said that staff did not pick up on this because I checked in at a kiosk
in Auckland (self-help terminal)