Qantas thinks they do, per https://www.qantas.com.au/agents/dyn...areInfoBaggage

Jetstar International Flights
Full bag connectivity and passenger check-in
QF International to JQ International v.v.
QF Domestic to JQ International v.v.

Baggage connectivity and passenger through check-in is available for customers connecting from/to Qantas domestic and international flights to/from Jetstar international flights. Passengers will receive boarding passes for both sectors at commencement of journey. This is available for both JQ marketed and QF codeshare customers.

Gotta love the consistency between QF and JQ, maybe they are trying to prove that they aren't owned by the same company

Obviously JQ domestic doesn't interline but NZ is JQi