Hi Labmsie welcome to the Business Travel Guru forums
Unfortunatly Qantas club membership does not give you priority check in on any Qantas partner, or Oneworld partner airlines (British Airways, American Airlines, Cathay)
This is also the case for Jetstar flights.
For prioriy check in on One world partner airlines, you either need to be traveling Business/First or be a Qantas Gold frequent flyer or above or Oneworld Sapphire (and above)
The only means of getting Priority check in on Jetstar is to be traveling StarClass. (Jetstar is not a Oneworld Partner, so Sapphire/Emerald status does not provide this benifit)
If you are planning any trips over to the US, I highly recomend flying American Airlines, joining their frequent flyer program and signing up for the Platinum challange, The Platinum challange basically allows you to obtain American Airlines Platinum status (Oneworld Sapphire) for a significantly reduced number of points/miles. After obtaining AA Plat (OS) you will get prioriy check in on all Oneworld partner airlines, along with increased mile and SC earning rates.
Ben Hoffman
The Business Travel Guru