I assume that you have a passport which allows visa-free entry into Schengen? Because you will need that.
QR flights are mostly on-time, but as they're usually flying the Dreamliner, delays do happen. Assuming that your flight is not delayed, your connection time should be plenty.
The QR flights normally arrive at gate F66. Go through the long corridor for arrivals on the fourth floor, and take the elevator or escalator down to the second floor, where you will enter Schengen (passport control). That's where you have two options:
1. If your bags are checked, go straight and go through the security control which is right in front of the passport control booths. Turn right after security, and go to gate F5, where you can push a button to call for a bus to take you to terminal 2. Be aware, however, that some people wait more than 15 minutes for the bus to arrive. The advantage is that, having done security in T5, you won't have to do it again in T2.
2. Go straight and go through customs (and pick up your bags first, if they're not checked through). From there, you can either follow the signs for T2 (it will be a 10-15 minute walk), or you can turn left and exit at the bus station. Buses "Alfa" (runs every 15 minutes) and "Beta" (runs every 8 minutes) will take you to T2 in five minutes. Actually, you can also take the express train from T5 to T2, but it's a bit more complicated to find it, and you may have to wait 15 or 20 minutes for the next train. At T2 you'll have to go through security and emigration.
I'm not 100% sure, but there may be a possibility of taking a transfer bus from gate F3 before going through immigration, which would be most convenient for you. I could check up on this next time I'm at ARN.
Which flight are you on? The morning, afternoon, or the new evening flight on the A330?