[MENTION=886565]WCE[/MENTION]: you can keep an eye out for cash upgrade offers. You will either see these during online check-in or the week before if you go to the Manage My Booking section on the QR website. You should be able to access a TA booking by entering your PNR and name.

Expect to pay around EUR 500 for the DOH-HEL sector per person if available - but don't know how the chances are given that its four people on the booking.