Baggage fee waivers are up to the partner airlines - no oneworld rules apply, as WestJet and Alaska aren't members.
On both airlines you'll have to pay for bags when booking the cheapest fare directly with them.
Alaska list their fees, and scenarios where they don't apply, at
Exceptions and waivers for our baggage policies | Alaska Airlines
WestJet list their fees, and scenarios where they don't apply, at
Service fees | WestJet
Neither page lists Qantas Frequent Flyer members as being eligible for free bags.
Note that WestJet has some more expensive Economy fares that include bags, while Alaska requires bags be added to all Economy fares.
If you're travelling either carrier on a QF codeshare this all changes, as you're on a "Qantas" flight and North American regulation states that the the airline whose flight
number appears for the
first flight on your ticket will determine whether its baggage rules or another airline's baggage rules will apply to all the flights in your itinerary. You could have AS or WS flight numbers for some short legs and have the QF allowance apply if your
first flight is on a QF flight number.
Note that, while a QF codeshare should get you free bags, it does not usually get you free seat selection and, like the baggage, you also do not get free seat selection when booking directly with the operating carrier.