If you are running a business, there are a number of legal requirements that you'll have to take care of. The size of the business doesn't matter. (The Australian tax department has a fact sheet on whether you are running a business or conducting a hobby).
Whether you’ve decided to start selling the clothes you design, you’ve just bought a franchise or you’re starting a company with 30 employees, you’ll need to register with the Australian Tax Office (ATO), apply for an Australian Business Number (ABN) or Australian Company Number (ACN) and, if you plan to trade under a name other than your own, register your business name with Consumer Affairs Victoria.
None of these are services provided by the City of Melbourne, but you can access them through the following links.
If you’re unsure which of these services you need, you’ll find a great deal of information at Business Victoria’s comprehensive guide for starting up your business. If you're running a small business, you may also be interested in the Small Business Mentoring Service.
Then, depending on the type of business you're running, you may need additional permits, either from Consumer Affairs Victoria or from the City of Melbourne: