You don't say how many of you are going and in what class but you could ask to be moved to the QR flight from EDI at 2.45pm and still go via DOH today.
Given the weather-related problems and cancellations yesterday with aircraft likely out of position I wouldn't be surprised if this isn't within the scope of UK261.
They do, however, have a duty of care so if you keep receipts for any extras then you should be able to claim those expenses.