Hi Clifford,I had a similar situation a few years ago when my flight was cancelled when QR were prevented from flying to Egypt.
I was assured by QR (by email and on the phone) that a full refund was in the process of being paid to my CC, but after a few weeks where nothing had happened, I called Amex to dispute and received the chargeback shortly thereafter.
QR has a lot of form in this area.
I have posted another thread on Flight Centre refunds also with Qatar flights. I initiated a dispute with my American Express card and they've credited back the two amounts. In my case the payments were made last September. I await feedback from Amex once they get a response from FC. I cancelled our flights late March and could not get any response from FC until coincidentally after I had the credits a couple of days ago, and had lodged another FC form on-line. Did you ever find out if QR followed up the chargeback with Amex? I'm curious to know, to judge how my matter will proceed. It appears FC hasn't been refunded by QR or FC is using my money for admin.