Both OP and wife should be able to use QR F lounge (Al Safwa) as they have one segment in first. I frequently do this with a much shorter F route and the DOH to LHR in J.

QR doesn’t allow Y guests in either J or F lounge, so need to use the generic FF lounges. Issue will be is OP’s wife won’t be eligible (as no status and the lounge is a status not J lounge) and the OP can only guest in one person. While you might think common sense would prevail, my experience in a similar situation was that it did not and QR wanted to split us all up. I think you can still pay for Y passengers as a guest into Al Safwa and Al Mourjan so that is probs best bet.