do you need a roadworthy certificate to transfer registration

Short answer: it depends on your state.

In Victoria and Queensland you generally need a roadworthy/safety certificate to transfer a registered vehicle.

In NSW, WA, SA, TAS and the NT you typically don’t for a straightforward ownership transfer, though you’ll still need the usual CTP/greenslip, stamp duty and ID, and some vehicles need an eSafety check for rego renewal.

In the ACT an inspection may be required in some circumstances (for example interstate transfers or where an inspection notice is issued).

Bottom line: check your state road authority’s current rules before you turn the paperwork into a pumpkin.