I never quite got people's grief with DOH's D/E gates. Especially with help from the travelators or the train, getting there is a matter of minutes. There are so many airports with way worse gate to gate time.
That being said, DOH's gate assignment does seem to be a bit random at times. I don't know many airports where planes as big as a 777 get the bus treatment that often, though there's definitely a connection to DOH's limited gate capacities. But just because a gate is empty at a given moment doesn't mean that it would have been free for the whole required duration.
And DOH and QR are definitely not the same company just because they share stakeholders. I often noticed subtle clues that there seems to be quite some rivalry between the two. After all, they are led by different people following different interests.