Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
"I just tried looking for MLE-LAX on AA site, but the only results I am getting is on BA economy. Am I doing something wrong?"
Yes: aa.com can only be used to check award-seat availability for about half of AA's partners. For QR, you can use BA's website to check availability on a segment-by-segment basis, and then call AA to book with AAdvantage miles. (Note that QR's DOH-LAX service is not yet in operation. I think it is due to commence in December or January.)