No, I posted in another thread that I do believe it's not possible no matter what. I had two excellent AA agents who tried everything -- calling oneworld liaison, calling QR themselves while I was on hold, and they said there was simply no way to do it.

That said, I was thrilled to figure out that you can use Avios and pay just 10% of the Avios for the infant ticket. So I got DOH-IAD for 70k per adult and 7k for the infant, total of about $300 in taxes. I had to book MLE-DOH separately but I just bought 3 coach seats for that (and QR allowed me to pick what look like PE seats on an ex-CX aircraft for free). But overall approximately the same net outlay with none of the hassle -- you can book QR w/ an infant easily on BA.com.