The fare buckets can be available on both the app and the desktop versions of Qantas Manage your booking after booking (not before).
I have a MEL-SIN-KUL return trip coming up with the SIN/KUL segments on MH in a non earning category - they show as '-' whereas the MEL Qantas segments show a 'O' . There seems to have some changes as Qantas used to show these fare buckets where they would not earn.
Looking at the same booking on the Malaysian Airlines web site "Manage Booking" shows the actual class 'O'. So no earn there.
You can do similar with CX flight bookings.
Also, there is the Finnair E-ticket tool which may send a copy of your itinerary to the booking's registered email address - this shows the fare buckets for each segment.
You can use this form to order your e-ticket receipt. If the reservation is no longer active, please contact our customer service.
www.finnair.com
This all basically can work because these airlines use Amadeus, so the booking reference is the same.