I note the previous two experts have opted out so I will try to finally answer your question.
There is no legal reason under Australian law why you would need to establish an Australian company to collect payments for an overseas based company. Indeed, if you did so you may find you in fact trigger certain tax obligations. For example, if you are providing services through your Australian based company then you likely should be charging GST on any sales in Australia and would liable for company income tax on any profits made by the Australian company. Whether this overall makes a difference to the overseas profit will depend on the overseas tax rules, but likely it will have some impact.
So the commercial question then becomes whether the marketing advantages of operating with an Australian company justify the administrative and tax cost of doing so.
Only an accountant familiar with your business can give you firm advice on the actual tax you may have to pay but I trust the above assists you in understanding the potential cost of establishing and collecting your Australian revenue through such a company, and accordingly, I would strongly recommend you engage an Australian Accountant to advise on the specifics of your proposed arrangement and to make a quantitative assessment of the costs and taxes of establishing and operating such an arragnement.
If you need help locating a suitable accountant the following link may assist you in finding a suitable accountant:
I trust the above assists.
Good luck and PLEASE RATE MY ANSWER.