I would wait until you have had a few good hot fires going and see what the adjoining areas are for temps.
I suspect that you will be modifying that wall on the stairs as others are suggesting before too long. Getting the heat to where it's needed seems to be a major topic on this forum. I also think that once you have been burning for a few months, you will feel much safer. IMHO drywall is no safety factor as the paper backing/paint are so combustible. A good stove system and safe competent operation are the answer to safety.
I suspect that you will be modifying that wall on the stairs as others are suggesting before too long. Getting the heat to where it's needed seems to be a major topic on this forum. I also think that once you have been burning for a few months, you will feel much safer. IMHO drywall is no safety factor as the paper backing/paint are so combustible. A good stove system and safe competent operation are the answer to safety.