Short answer: sometimes yes, sometimes no—because Australia loves rules with footnotes.
In Queensland, you must have a current Safety Certificate (roadworthy) before you advertise a registered car for sale.
In Victoria, a Roadworthy Certificate is required to transfer registration, and sellers typically supply it.
In NSW, SA, WA, TAS, ACT and NT, a seller-provided roadworthy is generally not mandatory to sell a registered car, though the buyer may need an inspection for transfer or at rego renewal.
Selling unregistered? You don’t need an RWC to sell, but the buyer will need inspections to re-register it.
Check your state or territory transport authority before listing; fines for getting it wrong are nobody’s favourite driving song.

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