Nizar,
I secured (from AA using my AAdvantage miles) a R/T business class award ticket for a friend, earlier this year: BKK-DOH-DXB-DOH-BKK. The DOH-DXB-DOH segments were in QR's 1st class cabin, in the same way that a business class ticket on AA will put you into the front cabin on a 2-cabin domestic AA flight. I am surprised that Qantas put your parents into economy for those short, 2-class segments and I would suggest that you make inquiry to determine what is going on. (I would also ask Qantas what they would do for a business class award ticket SYD-LAX-LAS on the LAX-LAS segment which AA operates with only First and Economy class.
Good luck and please provide feedback if you do speak with Qantas.