An update after 20 frustrating minutes on the phone:
Attempt 1: Select the menu option for Qantas FF enquiries: Get a recorded message saying Star Class and Jet Flex earn miles and SCs, then get hung up on.
Attempt 2: Pick the booking enquiry menu option. Speak to a hassled sounding guy who at least tried to be helpful.
His first response: You'll be on a "little plane" for the domestic flights, so no *class.
Me: I understand that's the case SYD-MEL, but MEL-SYD is ex int'l terminal on an A330.
Him: Hold please sir (I was to hear this a lot...). But sir you ARE in star class.
Me: Why then does my itinerary say Jet Saver?
Him: Hold please sir. Our records say you ARE in Star class, in fact you have very good seats, 24 A and B. I'll re-send your itinerary.
Me: Umm...good seats for whY maybe, but rows 1-6 would be better ;-)
Him: Hold please sir. Oh I see that Star class is fully booked on this leg, so you were allocated very good whY seats in the most expensive fare category
And on it went.
I thanked him for being as helpful as he could, and asked to speak to his boss.
The supervisor was less helpful, and more argumentative, talking over me at times. He also tried to tell me that the *cabin on JQ37 SYD-MEL was full. (It's not, a dummy MEL-DPS booking on that flight reveals only 2 seats allocated so far). Back and forth dialogue went nowhere until he stumbled on the idea of saying that my star class promo fare isn't quite star class and all those empty seats are for proper star class pax. (Of course the website doesn't give the option to book a non-promo fare if there's a promotion on).
I gave up on the seating - I'll take the argument to customer service in a letter. I then asked him if I'll earn miles and SCs for the SYD-MEL and MEL-SYD tags. After being on hold for a few more minutes he said yes - but didn't sound 100% sure about it. Again, it had clearly reached the point where he wasn't able to help any more. I thanked him and said I'll take it up with customer service.
Not holding my breath on a useful answer from them either, but this flight is still 6 months away, so I've got plenty of time to just chip away and see if anyone at JQ gives a stuff about their (supposedly) premium pax in Star class.