Hi Jo
My understanding is that there are two issues there.
1. Registration. As you already have NZ registration (and you have a current APC in NZ? - you'll need that) then you are able to apply to any of the state registration boards under the Trans-Tasman Mutural Recogntion agreement. You will of course have to meet the other requirements for registration with that Australian state boad - eg have professional indemnity to the minimum amount oganised.
2. Immigration - I don't know about the Australian immigration requirements for working in Australia for UK citizens. So you would just have to proceed with that as required.
You are right about the lack of work in NZ - completely dried up and probably it is going to get worse before it gets better.
The job market in Australia is completely different - the world is your oyster there!
So my advice is do what you can to get things started for a job in OZ - may be you could check out NZ later in the the piece - if you are on a working holiday - maybe at the end.
Best of luck with your plans.