I'll have to look into this a little more because I am just not certain on what this rug is.
I'm not saying this is Qashqai, because I do not believe it is. What I do know is that Qashqai are not always wool pile with wool foundation. Many older ones are, however, most newer Qashqai rugs are wool pile, with cotton foundation. I personally own a Qashqai from the 1960's early 70s that has a cotton foundation. Gabbeh design rugs woven by the Qashqai are also woven on cotton foundation. These are made by nomadic weavers, often migrating several hundred miles every year back and forth. I do not think this is Qashqai, but the statement that Qashqai rugs are wool foundation is incorrect.
It seems inevitably, when some rug dealers cannot isolate origin, they call assign it the name Hamadan because Hamadan covers such a broad, large area of Iran. While it may be the case that this rug is a Hamadan, I'm just not certain, but it's probably a decent guess. The design would say it could be, but looking at the back of the rug tells a much different story: What I can say is that hamadan often has single weft weaving. Simplified answer to what this means, the appearance of knots on the back of the rug. They will be oriented in almost a diagonal fashion, seemingly alternating columns of knots. This rug does not exhibit this orientation, not to say there's no possibility this is a Hamadan, it could very well be.
I'll do more research and get back to you