Layover in Melbourne, can we get out?

We have done this in Europe so is it something mandatory in Australia to receive the luggage if we want to get out???

No it is not ... if your luggage is checked through then that is fine.

To get out we should simply pass the customs and immigration and it should not take much. last time we did this in Vienna and it did not take 5 minutes.

It might take more than five minutes ... but it isn't as dire as the above post makes out ... the walk is more than five minutes on its own, but overall it won't gouge into your nine hours too much.

The biggest delay on arrival into Melbourne is usually collecting luggage from the carousel - and this will not apply to you. Allow two hours to re-board for NZ - no more than that is necessary.

Arriving at 9.25 am is a lot better than 6 am and 18 Nov. is just after the Melbourne Spring Racing Carnival, the Melbourne Cup you have missed by 11 days but it is a time renowned for gardeners at the track having roses blooming right on time and gardens around Melbourne ought to be looking their best.

As for the checked luggage, I'd just double check with your airline that it is checked through for you and my allowance of time for exit etc. was just in case it is not checked through but with your backpacks and even if having no luggage, you are still subject to customs and will have filled in an arrivals card as you are accustomed to.
You can either have things to declare or not but either way you can still be selected so as far as what you may have, even stuff like snacks needs to be declared as food, even a piece of fruit from the plane needs to be discarded in bins provided on disembarking.

If you have things you should have declared and forgot and get picked for inspection, you could be up for some time to clear customs.

As for the City Circle Tram, it as far as I know from past use no longer goes down Spencer Street outside the Southern Cross Station so unless that has somehow been changed back ( which the route does not indicate ), you can walk a couple of blocks south, flat and then downhill to Flinders Street and you will see a stop there to the left at the intersection.

I would not get too ambitious with tavelling too far out of the CBD as like over to St. Kilda for time flies quickly when you least do not want it to and then you can be in a rush to get back to the airport, a taxi then the best option so perhaps if you use Skybus to go in, you might just consider getting a one way ticket.

So long as you aren't connecting to a low cost carrier, its pretty safe to assume your baggage will be checked through to Auckland. And unless your backpacks are small daypacks, consider checking them in as well.

It is Air New Zealand, I think we should be fine, I have baggage delay insurance too, so if they lose it or there is a delay I should get some cash

Air New Zealand haven't won awards for nothing. They are consistently among top airlines.

It is kind of difficult to know what to recommend in terms of what to do since there is a limited amount of detail on your interests but Trav has given you some great options.

Here's some options.

1)The City Circle tram is a vintage tram which is free (as are all trams within the CBD grid, as mentioned). It is quaint and does an okay loop and goes past things like Filnders St station, Treasury Building, Parliament house and some other important buildings.
2) A walk along both sides of the Yarra will give a particular impression of the city. Start at Princes Bridge and go east through Birrarung Marr park and back over the river and west through the Botanic Gardens and over St Kilda Rd and through Southbank and either back over the river before or after the casino. You wouldn't want to do it in pouring rain and November is one of Melbourne's wettest months.
3) If you want some Aussie art the Ian Potter gallery is free and has some fine and accessible examples. It is on the corner of Filnders St and Swanston St.
4) The Queen Victoria Market is great.
5) I don't regard Melbourne's CBD as being best for restaurants but there are less expensive Asian options on the north end of Elizabeth St, good Chinese in Little Bourke St between Swanston and Exhibition St (my favourite is Supper Inn in Cellestial Ave, it is 'genuine' and rough around the edges) and especially Dim Sum for Saturday lunch. If you want to spend $30-40 for a main you will have lots of choices.