Join Date: May 2008
Location: IAD or elsewhere
Programs: UA 1K, LH M&M, AA EXP, Marriott Plat, Avis NotLast, Hilton Gold, Hertz 5*
Posts: 655
If you could get QR to add your MP # to your PNR, either beforehand or at the airport, then then chance of getting credit quicker is possible.
After the fact certainly you can call, but MP will want hard evidence of the flight. I do not know if they will be able to see your past intinerary, unless you were flying on a UA codeshare (as some QR flights are).
Unfortunately, there is no standard timeline for crediting. Could be 24 hours, could be 2 months, could be never. And since QR declined to do it preflight, the chance of them taking interest postflight is practically nil.