No. There is no such requirement for an Australian student visa.

The current Visa Application Charge for a student is AUD$630

Student visa holders can also temporarily work over their normal limit of 40 hours per fortnight during term time across all sectors of the economy. Students are able to work immediately upon arrival in Australia, and do not need to wait until their course commences.

There is no limit to when you can submit your student visa application. It is recommended that you lodge a complete application at least eight weeks before your course commences.