Needs to be booked as LA flight numbers / LA operated in order to qualify for the Avios. QR operated isn't eligible under BA rules for these particular flights, although you may get lucky as a result of an error in your favour - it's not meant to happen.

Crediting to QR Privilege Club would work. You can then transfer the points over to your BA once they credit there. Tier points wouldn't be earned on LA anyway so it's just the Avios at stake.

LA is also notoriously slow in posting Avios to accounts so anticipate for it to take the full 28 days and retain your boarding passes incase you need to make a post travel claim for missing Avios.