If they will through check is on QR, so you need to ask that question specifically there. I can say that on the way back IB/I2 will not through check to the QR flight.

That's plenty of time for a connection assuming nothing goes wrong and you do get luggage through checked. Even without it, it should still be viable. The bottleneck is usually in getting luggage from T4S at the main baggage reclaim area. You need to expect that to take an hour, but even so it should be okay.