The Qantas website might work if you enter the booking reference and last name.

https://www.qantas.com/gb/en/manage-booking.html

Hopefully this brings up the screen with flight details. If you scroll down to the section on flight details section and then click on each flight I think it should expand to give more information about each flight. In the travel class, it should give the letter in brackets after the cabin e.g. Business (I)