I'm at DOH and can strongly say that things are NOT operating normally.
Even via the lounge I was in a queue for 4 hours to get a replacement flight, and I joined it sharpish when my flight was finally cancelled. Still huge queues in the lounge which seem to be taking c.20-30m per passenger (mostly including calling a ticket desk, often people struggling to get through to ticketing). The queue at transfer desks and for help outside are crazy long it's hard to overstate.
Limited departures from what I can tell this morning. The excuse from the lounge is that planes are in the wrong place - quite jarring to look out over an airport which has planes parked at every gate and none seem to have moved. My replacement flight was due to have taken off already but currently still no gate (or even acknowledgement, it does not even say "delayed") on the info boards.
I have to say that QR's handling of this has been absolutely atrocious. No information at all last night (even saying flights were delayed, they just sat on the departure board long after they went). Essentially no way to get help other than joining some of the longest and slowest moving queues.
I'm pleased to be on the world's best airline... (24h awake and counting...)