As an example, if someone took the c.9am flight from BKK and arrived DOH c.midday, they would have to wait 13-14 hours for the c.1.30am departure. There is not an earlier departure ex-DOH.

BUT as pointed out, later flights ex-BKK would connect with the same flight ex-DOH with only a couple of hours wait. So picking the 9am departure would not be eligible for stpc as several itineraries with shorter connections are available. Choosing not to book the shortest journey is the customer's decision, irrespective of price. STPC is for those passengers who have no other choice but a long connection (eg. Only one flight opertaing per day on each sector).

There is often a trade off between the cheapest fares and the shortest connections. Presumably the OP got a comparatively good deal buying a P fare, so stumping up $30 for a hotel hopefully won't hurt too much.

It seems to me that QR responded quite promptly to the stpc enquiry here.