I assume you booked via BA if you're quoting their flight number? That should be a big enough change to allow rebooking onto an alternative flight with a shorter connection.

You almost certainly wouldn't be due any compensation under UK/EU261, as you'd be arriving at your final destination on time. Then there is the reason for the schedule change etc.

And Qatar don't give out gestures of goodwill generally speaking. As the flight is imminent you could go to the hotel desk in transfers at DOH and explain your case to see whether they'd provide a hotel.