Hi Olybeast - the first connection is just under the 8 hour mark so there will be no assistance from QR as far as I understand. From what I have read there is an airport airside at the new HIA so you could check in there without needing to clear customs.
On the return leg your layover is more than 8 hours and assuming there is no earlier connection you should be eligible for a stop over hotel. I am flying in October from IAD - DOH - CPT arriving in DOH around 18h20 and departing the next morning at around 06h45 and they have sent me through a voucher for the Oryx Rotana and return transfers.