Upvote:1
This page should help. While it does not list Air New Zealand as a Codeshare Partner in the Asia-Pacific section, it does mention down the bottom right that Interline Partners also enjoy:
seamless connectivity and through-baggage check-in.
https://www.qatarairways.com/en-au/partners-codeshare.html
However, I understand that this does not specifically mention Air New Zealand. In the unlikely case that you need to re-check your bags, you would claim your bags from the baggage carousel and then take them to the transfer counter or check-in so they could process them. You would likely already have your boarding pass, either way.
The Air New Zealand website mentions that there is no way of knowing until you land in Melbourne.
However, some countries, like the United States, still require you to pick up your bags, go through customs, and re-check them at a transfer or check-in desk. Aside from America where it's always mandatory, the only way to know for sure is to ask at the counter when you check-in at the airport.
If your connecting journeys are separately ticketed, you will indeed need to check in separately for each one, collect your bags and re-check them in between.
Of course, it is all on one ticket, so the second part does not apply. The only way to confirm would be to call the airlines - but whatever happens, if you have to, you can check when you land in Melbourne and you should have time to do so (2 hrs 5 min).
https://www.airnewzealand.com.au/checked-in-baggage#connecting
Hope this helps!