Booked on Qantas flight as American codeshare - how do I get a points or paid upgrade?

I’m new to the world of FF points and Point Hacks and was wondering if somebody could give me some advice.
I booked a flight on AA (operated by Qantas) from AUS to US. Fare Code is ‘S’ - whatever this means. Now I was just wondering if anybody knows a way to get an upgrade to business class. Either by AA or Q points or $?
Much appreciated!

Unfortunately you’re out of luck here. Although you have booked on a Qantas flight, as an American codeshare I don’t believe you are eligible for a points upgrade with Qantas Frequent Flyer. You also can’t use American miles to upgrade codeshare flights, to my knowledge.

Someone correct me if I’m wrong…