I think this arrangement would raise a few eyebrows with Australian immigration and the Australian taxation authority. If you are on a tourist visa to Australia, they will be wondering how you will support yourself. If you are a young and working age person, they will definitely be questioning you about employment and income.
What is confusing to me is you wanted to avoid double taxes, does it mean you will have proof that you will be working in Australia so you will be paying taxes in Australia? But you also said the company does not have an office in Australia, then you will not be working officially in Australia, thus the raised immigration eyebrows mentioned above.
Having your income sent to Australia sounds very dicey to me. Officially you will not be working in HK, therefore, no income here and no taxes to be paid. But is your employer not going to declare your salary as corporate expense and you as the recipient?
Whatever arrangements you make with anyone, don't leave any trace on your cell phone because that's the first thing they check at immigration if they suspect anything. They will also check your computer too. Paper trail is now the electronic trail.
Explore your options thoroughly before you embark on this adventure. I hope you do get what you want after figuring things out. I hope there will be positive information for you from other responses.