It is my understanding is yes they do earn on Jetstar flights as long as it has a QF flight number. Had flights to Nadi recently operated by Fiji Airways with QF flight number and it worked.
"this promotion means any Domestic or International Qantas operated flight with a QF flight number on your ticket where Status Credits are normally earned."
# Status Credits are earned on eligible Qantas, oneworld alliance airlines, Jetstar Airlines and Fiji Airways flights only - see the
Airline Earning Tables. for details.
But who knows after all the inconsistent experiences people have had with QF on this issue.