Looks like the 787 pilots are not spared the very late night flights.
I guess the A320 pilots transitioning to the 787 will already be used to those flights.
From the QR website:
Qatar Airways Boeing 787 Dreamliner flights
from 20th November to 31st January 2013
Doha (DOH) to Dubai (DXB) - Daily
QR102 Depart Doha at 01:10 Arrive Dubai at 03:20
QR106 Depart Doha at 08:00 Arrive Dubai at 10:10
QR116 Depart Doha at 13:20 Arrive Dubai at 15:30
QR118 Depart Doha at 18:40 Arrive Dubai at 20:50
Dubai (DXB) to Doha (DOH) - Daily
QR103 Depart Dubai at 05:45 Arrive Doha at 05:55
QR101 Depart Dubai at 11:40 Arrive Doha at 11:50
QR117 Depart Dubai at 16:55 Arrive Doha at 17:05
QR119 Depart Dubai at 22:05 Arrive Doha at 22:15