you have asked a question that is changing by the month here at QR with the A-330 fleet growing and the A-300 fleet due to shrink in a few years with the coming of the 777. Also the average hours per month is a joke when it comes to all the different fleets with A-330 guy/gals doing 85-90 hours sometimes close to 100. The A-300 fleet doing anywhere from 45 to 75 hours a month and the A-320 guys hovering around 60 hours max a month with massive time away from home.
There is no longer that Singapore, Cebu flight as we now do that trip on the A-330 fleet.
The average amount of nights away from home can vary if you are a training captain or not. As a training captain you will be in Doha many nights but as a line pilot you will have as A300 MAN said, 12 days or so out of Doha but you will have to remember that you start many flights late at night and I am not sure that will count as a "night at home" as you have asked.
CMB
MUC
FRA
MXP
IST
KUL*
SIN* (now on the A-330)
CEB* (now on the A-330)
TRV
HYD
AMS
CMN (now on the A-330 back and forth i think)
DAC*(now on the A-330)
MLE (dead-heading or positioning layover)
ZRH
KTM
BKK
FCO
AMS,MUC and MAA are QR Cargo layovers.
and don't forget DXB for the simulator.
I would think that trying to base your decision on the route structure of a fleet is not a good idea as it will chop and change in a few weeks,months and for sure years.
Good Luck
HM