Yes, it's acheivable.

Doha is built for Transit, and Qatar build their schedules with two significant banks of incomng and departing flights, and every day many thousnads of passengers will successfully transit Doha with connection times at or around MCT (45mins) with no issue.

I would not be overly worried for a bus gate, it really depends where the plane is, if you do or don't go through transit security (with a bus gate that's more of a certainity), and where your departing gate is. Having a plan of the airport so you can quickly orientate yourself can help where the minutes you have to get you your next flight are tight, there's one available on the airport app and last time i checked it doesn't need network access to use it.

If you arrive on an airbridge, if your flight is selected in the flights-today-permitted-to-randomly-bypass-transit-security you will be tipped out directly onto the main concourse in which case you have just won back a few mins and can go directly to your gate, via any of the airport facilities if time permits. But if there's an escalator that's 2 or 3 floors high beyond the airbrdge going up about two floors, you now needs to walk to transit security, which could be a longish walk if you're at a high number C gate. The transit security is located above the main interchange concourse where A, B and C concourses intersect. Bus gates usually deliver you to a door with a very long escalator (4 or 5 floors up) but its adjacent to transit security and hence that eliminates a long walk.

At transit security, if you are pressed for time, being polite and asking forgiveness to jump the queue (approach staff with good grace for permission) is usually a good strategy. As you exit transit security you descend down to the main concourse where A B and C intersect and the big teddy bear is parked.

If you any reason you do miss your connection, QR will take care of your either on their next DUB flight which will be 6 or 7 hours later, or if you politely stamp your feet and assert pluasible reasons why you need to be in DUB asap a possibility would be a reroute onto London and a connecting flight with BA to DUB.