Flown the DOH-DMM leg of that route many times on KL. Pretty smooth check in at DOH, as I remember. If anything, if you get there too early (more than 2-2.5 hrs) they aren't ready for you to check in anyway, and then haven't yet opened the gate (there is a holding area at the gate for this flight) once you get through security/immigration. There is a priority check in line but as with most airports in the region that doesn't always mean much.

As for security and immigration, those have been hit and miss for me in DOH. Some nights quite crowded with guest workers headed home or transiting pilgrims.

You'd be taking a risk, but not a huge one.