Good suggestion to post on the QF board. I got the following relevant reply:

Back the OP's concerns (and JQ58 is DPS-DRW-CNS - which has nothing to do with Jetconnect!) I think this could be tied in with recent changes to classic award availability ( in the QFF program) on JQ flights.

Prior to this recent change (made on 8th April), QF redemptions on JQ had to be booked as ASA's or on the QF code on the JQ flight. Now you cannot book QFF redemptions on JQ on a QF code - ONLY on the JQ code.

What else have I noticed?
1) QF code that sat beneath JQ operated flights on Melbourne Airport website (flight info) has disappeared recently
2) Oneworld used to show QF codes on some routes as QF* operated by Jetstar (eg DPS-DRW). Now it shows nothing on such routes.

This points to a conclusion that QF codes on JQ flights have been dropped/removed/eliminated for new bookings. Something many would think is a good idea, but obviously there has been some collateral damage to people like the OP.

I think the overriding question is whether this QF change to their program was meant to have consequences of a much larger scope affecting OW partners from booking the JQ-QF codeshares (that apparently no longer exist). I'm still waiting almost one week to hear back from the AA supervisor (got their email).

The other aspect of concern to me is if this is in fact a permanent change to all OW partners' ability to book the former JQ-QF codeshares, shouldn't there have been some sort of warning in "Program News" or wherever AA puts those sorts of program changes?