QR is responsible, assuming this was all on one PNR. IATA rules states that it's always the last carrier who handles missing baggage claims. While it may not be "QR's fault", it doesn't matter as far as the passenger is concerned.
I assume the baggage was checked through to
DPS? And that it wasn't short checked such that you'd have to pick it up somewhere along the way?
The logic for this is sound. In some cases, the other carriers on an itinerary may not even operate into the airport that is your final destination, making filing a bag claim impossible.
See
https://www.iata.org/contentassets/e...-interline.pdf.