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Yes, Qatar accept transit through airport. I recently went via qatar airline with no issues on RTD without PR.
Also if you’re using Qatar airline then it offers free hotel stay and meal vouchers within airport if your transit is more than 8 hours. Only thing is you have to pre-book accommodation on their website once you booked your airfare (only with Qatar airways). My stay was 17 hours and 20 hours on my way back ( you can transit upto 24 hours without any hassle).
Did you buy a ticket from qatar airways website? If yes what did you write in Nationality?
 
Generally Qatar does not accept entry with RTD. Inorder to enter Qatar with RTD, you need special permission from the ministry of interior. Very long process to get the special permission, but i only know of someone who was granted special permission to enter Qatar with RTD.
How to apply to get the special permission? Please i need the steps and how long it will take for decision?
 
There is an option to visit Qatar on Haya portal holding Travel Document, I applied and stated no nationality (my mistake) and my application got stuck for the past few months. They are not accepting or rejecting the application. Can not make another application unless gets the primary application decision.
One`s should try to add nationality Canada and i hope they will issue they visa on Travel document.
I sent email to qatar embassy and I asked them about visa for Canadian rtd and they replied they dont issue visa for RTD from embassy and they said for my original nationality I dont need visa if I travel by my seized passport.by the way I am not PR yet just wp and NOD.
Regarding haya visa i just know about it from you now.should i mention my original nationality? Is there option for issuer country of RTD ? do you know someone travel with RTD and haya visa ?