As Tokyoite pointed out, you need a plating carrier who can include both TK and QR in the same ticket. But the plating carrier does not necessarily have to be TK or QR.
I once needed to fly ICN-IST-OTP (with ICN-IST on OZ and IST-OTP on RO), as a one ticket (because of the checked luggage). OZ cannot issue tickets on RO and RO cannot issue tickets on OZ, but Hahn Air was able to issue a ticket including both segments (169-XXX ticket). However, AFAIK Hahn Air do not work with retail customers, only with travel agents, so you would need to find a TA who can ticket it (again, assuming the TK and QR fares can be EOE combined, as Tokyoite advised).