Yup - the question always hinges on:

1) How easy is it to find a free, pleasant, camping spot?

In NZ pretty much every piece of land is somebody's property and being actively looked after, and if it isn't, it's a conservation area where camping is probably actively forbidden outside designated areas. So tenting probably won't be free. I imagine in the wilder parts of Australia this is not really enforced much, but the issue of camping safely, having access to water, etc. is still a big concern.

2) How hard is it to find affordable indoor accommodation?

I don't have experience traveling through rural Australia, but I imagine there are hostels/roadhouses at the same places where you would stop anyway to get fuel.

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What's definitely not worth the headache is bringing your camping equipment from home. When I was last in NZ, and scheduled a 4-day hike in the Abel Tasman national park (could've done it in 3 easily, 2 if I pushed...), I paid something very reasonable - 40 dollars I think, in total - to rent a big 65-liter backpack and a sleeping bag from a local company. They delivered it to my hostel in Nelson and picked it up from there too. And for the sleeping bag, I could have just picked up a cheapo one from a big supermarket for like 30-40 NZD if I was precious about a used one. In fact, many backpacker hostels in NZ - especially at the logical start/end points of a trip - will have a "free gear" pile.

So if I was the OP, I'd get some basic cheapo camping gear to bring along on the trip and use where it makes sense, but assume I'd stick to indoor accommodation mostly.