QR do codeshare with PG so they may be able to book through. You can certainly ask about interlining.

However, in BKK, you'll be in a different area of the airport so don't expect access to the Qatar lounge (which is the Thai Airways international lounge).

There doesn't appear to be any way to do a BA (or other OW codeshare) on PG unless combined with an international long haul fare and this is borne out by an ITA search.