gnomey a warm welcome to the QR forum.
With regard to arrival and departure gates the standard reply is 'No one knows' Unless it has changed in the last few months then arrival and departure gates are allocated in an almost random fashion. And there is no guarantee that you will have a contact gate. Due to the lack of contact gates remote stands are frequently used, even for the larger aircraft. and just because your connection left from D4 yesterday it does not mean that it will today.
Having a remote stand on arrival can be an advantage since buses will transport you to the foot of the stairs leading up to transit security or in a few cases each day directly into the departure areas and you will avoid the long walk to security.
Each day Security prepares a secret list of flights that will not be subject to security screening on transit. If your flight is on this list you will be deposited at the entrance to the departure areas. If not, then at the foot of the stairs up to security. The list changes completely every day so there is no way of knowing beforehand.
I personally would allow at least 20 minutes to get to the furthest gates unless you have your running shoes on!
Do take a look at the QR dashboard widget
http://www.flyertalk.com/forum/qatar...h-airport.html. It contains a wealth of useful information and tips.
Please remember that access to Al Mourjan is restricted to those travelling in J.