There isn't any official protection on separate tickets. Checking in for both at the origin saves you some time rechecking at Doha. But if you no show for the second flight, officially you're on our own.

BA don't refund redemption cancellations within 24 hours of departure, whereas QR will refund 3 hours before, so potentially there’s some benefit to booking it through QR rather than BA.

Either way though, if you're delayed to the extent of missing the second flight, you are most likely looking at either buying a new ticket, or hoping for a hens teeth customer servce gesture.

Separate bookings means accepting the risk if things go wrong.