The work restrictions on a student visa are under condition 8104 which states that primary applicants and family members of Subclass 500 visa holders in Australia can work up to 48 hours a fortnight and only after the primary visa holder starts their course. Exceptions include if the family member or primary visa holder had a prior visa allowing work. If the primary visa holder is pursuing a master's or doctoral degree, family members can work unlimited hours. If the primary visa holder is completing a master's degree by research or doctorate degree, the primary visa can work unlimited hours. Work is defined in the regulations as an activity that, in Australia, normally attracts remuneration. Technically, remote work with an overseas company would meet the definition of work in the regulations if the work activities are conducted in Australia. Despite the above, it may be worth noting that under visitor visas which have a no work condition, immigration policy states that visa applicants intending to continue online work (including social media influencers and bloggers) while visiting Australia for short stays would generally not be considered in breach of the no work condition, unless being paid by an Australian organisation (for example, an applicant receiving remuneration to attend a promotional event in Australia). It is important to note that this is intended for short visits under the visitor visa, and not necessarily extended periods of stay under a student visa. I recommend you contact a registered migration agent (such as myself) to raise a complex policy query with the immigration department in Australia to enquire if they are willing to offer a policy position on remote work in this kind of situation.
