Multi-airline trip booked through one airline - who to call if problems?

I booked a trip through Qantas that has me flying outside Australia on other oneworld airlines.

If I'm on the road and (say) weather hits and a flight of mine gets canceled, who's better to call - Qantas or the airline I was due to fly?

One possible factor: I do have top-tier status with Qantas, which does mean I've got access to a dedicated team inside their call centre.