Unfortunately, it looks like
there are no QF bereavement fares on international routes, but there are on domestic routes in Australia.
get some help from AA. They have domestic/Canada bereavement fares, but their website tells the story on AA codeshares for QF flights: "American Airlines offers bereavement and compassion fares for travel in the case of death or medical emergency. The information below pertains to travel within the 48 U.S. contiguous states, Hawaii and Canada. Since most international fares are regulated by foreign countries, bereavement fares are technically not offered, but customers may obtain assistance by calling American Airlines Reservations."
From a very basic search on the AC and UA forums for the word "bereavement", it looks like AC offer international bereavement fares but the pricing may not be very attractive, but that UA may be an option.
For QF, it looks like your best bet is, if you have the points, to call QF and try and get a seat opened for you if none is available for the days you need.