In J you will have no problem whatsoever! When I flew LHR-DOH-MEL last year in J, I had a 50 minute connection. However we were at least 30 minutes late landing, then the PT bus went to the arrival terminal first, then to the Premium Terminal. I went through security and straight to the gate, through security again and then sat on the bus waiting for more passengers for about 10 minutes. It was absolutely fine.