Iranian airspace is currently closed to all commercial traffic. Even once it might reopen partially every flight operator would be doing their own risk assessments of what route a specific flight will take, considering weather and expected head or tailwinds, known turbulence, airspace availability, availability of diversion airports and combined with the load characteristics of each flight, not only the number of passengers but also load and risks presented by loaded cargo. It also results in the required fuel for the flight including any extra fuel required for potential diversions.

There's a dedicated department doing these calculations for each flight, agreeing them with the flight commander, submitting the preferred commercial route to relevant ATCs on behalf of the flight commander.

Qatar have considerable experience of needing to avoid airspace, they've been doing it on a daily basis for parts of the middle east and Africa for a considerable time, and even had to avoid Saudi airspace for many months, and are used to putting extra fuel in planes and taking longer routes.

You have nothing to worry about. They are risk averse and have a strong reputation to maintain.