Welcome to the forum margarietta and you do certainly have limited options.

Probably the simplest path for you would be to apply for a 12 months tourist visa - Tourist Visa (Subclass 676)
If you have sound financials that can show you can support yourself, there should not be a problem with getting one - only issue would be whether they look for a lump sum availability rather than an income and you do not have the former though having accommodation here will be in your favour.

On getting such a visa it may be that you do not have to return to the UK to apply for a partner visa for it could be possible that you could initially apply for a tourist visa extension - some visas get what is called a "no further stay" condition placed when granted but if your initial tourist visa did not have that [it's a condition placed somewhat randomly] , should be possible for you to get an extension.

If there was such a condition, you could look at taking a quick trip to NZ and apply for an ETA to return - Electronic Travel Authority (ETA) - Online Applications

One way or the other, whether with an extension or being back with an ETA you could apply for the partner visa while here in Australia.

You could look at going back to the UK after having been here for 12 months and perhaps have no problem though it could come down to what the department considers "immediately prior" re the clause under eligibility There is a whole immi section on the "One Year Relationship Requirement" and worth a read for you because things like sharing financials etc. all come into it as you'll see.
Though you could be living together, it will be I presume in your Aussie guys residence as his guest/partner and that may create at least one aspect to be dealt with.

So if I was you, I'd have the Aussie guy for starters ring immi up here in Oz and have a chat with them re meeting the particular requirements given what the situation may be, and see if he can arrange an interview would be even better.
It could be that it may be advised for his utility bills to be put into both your names for example and you run a joint bank account for living expenses, ie., do as many things that immi are looking for that will define a relationship.

And he could also see if he can get any sense out of them in respect to you returning to the UK before applying and of the "immediately prior" bit.

So if you have that part sorted so as to have a plan to be implemented on arrival for 12 months, and there is no "no further stay" applied to your visa you can then seek an extension and subsequently apply for the partner visa.

The other approach after an initial 12 months or even if there is difficulty in getting 12 and they for instance only give you six and say maybe a three month extension would be to consider your commitment level, ie. has it worked out as you hope and are you both prepared to tie the knot! - for then there's the prospective marriage visa [details in the family section where partners visas are].

You get 9 months to do it and so you'll have had a reasonable further length of time to decide.

There are also what are called Investment Retiree Visas, essentially where you buy your way in by having a kitbag full of $$$$, much more involved though.