More than enough, assuming your inbound is on time. Min connect time at DOH is 45 mins and it practically possible in less. With that connection I would spend 45-50 mins in the lounge.

If you misconnect due to QR's fault, they will put you on the next available flight and give you food and accom as necessary.

DOH has lettered concourses in a vaguely star layout, with the lounges, etc at the centre. Just check the screens as you arrive for your next gate. Gates close 20 mins before departure.