It's certainly not good haha. I think that's super risky. And you're right to point out that risk and say it may be stupid. But it still isn't addressing the OP's question, which was not "will I have to pay?" or "will I be protected?"

He says he has 90 minutes to transfer from a DOH-BEY flight to a BEY-DOH flight, which leads me to believe that he's trying to do a turnaround on what will probably be the same QR plane. So if the incoming is delayed, the outbound will be delayed, as well.

Either way, for the OP's purpose, just ASSUME everything goes according to plan. How easy/difficult is it to do the transfer? Even under the right circumstances, how likely is it that the OP will be held up and miss his flight?

The purpose of these threads isn't to prove you're smarter and more experienced and to tell the OP he's being irresponsible. If you want to advise against it, do. But at least try to be helpful. And if you don't know, just say so.