I wouldn't be comfortable assuring someone that through check-in of passengers and bags on separate tickets is fine. It might well have been, could be still. But these are strange times, and QR procedures can be terminated or changed at whim.
Carriers in the revenue boosting phase QR has entered might realise that making a two-ticket journey near-seamless isn't in its interests.
The quid pro quo of saving cash on separate tickets is acceptance of a measure of inconvenience: I'd suggest that should take the form of a comfortably extended connecting interval at Doha to lower the risk of misconnection and allow for the chance that the airline doesn't play ball with through bags. Best of all, hand-baggage only!