I think the highest lounge you could buy into with cash on a (P) fare would be Al Mourjan. I'm not sure if you can use avios to buy lounge access though (others may have direct experience).

Just as an alternative possibility, you only need one transaction (spend or earn) to go through your QRPC account before December to extend all of your avios for 3 years. So if you credit your upcoming flight to QR your avios will be automatically extended. Alternatives could include flying on or redeeming a partner flight, buying something through one of the shopping partners (including many hotel chains), or buying the minimum number of avios.