Originally Posted by JJeffrey

No, you cannot use AA miles to upgrade on QR.

You might be able to transfer AA miles to QR using a 3rd party site (like points.com) however it will most likely be a horrible transfer ratio (think 100k AA miles will equal 10k QR miles, for example). And of course you'd need to research if an upgrade is even a possibility using QR miles, how much it would cost, etc.

QR can at times offer decent discount business fares, far and away the easiest avenue to upgrade will be to call QR and see what it would cost to upfare to business class.