Yes, you can do business on a student visa in Australia. However, on a student visa, you can work a maximum of 20 hours weekly during the term. Moreover, you must also meet your studying requirements so as to not violate the student visa requirement.
To establish any business, you must register through the Business Registration System to receive the ABN. Following this, the procedure differs depending on the choice of business structure. If you want to start a Limited Liability Company specifically, you must formally register the company through ASIC. However, for this, a local resident director is required.