Very beautiful!
I'm not an expert, so the following are guesses only. Wait for the experts to confirm (or correct) what I say.
This type of rug is called a Beluch (or Baluch or Belouch, etc.), after the tribes (Beluch tribes) who make them. It's a tribal rug. The Beluch tribes were not restricted to Beluchistan but were living (as Nomads) in various parts of Iran.
The border is a typical Beluch main rug border design, and the field is a typical Beluch main rug field design.
This rug looks compatible with being Beluch, except that you would expect (1) a similar kilim end on the other side and (2) the selvages to look different (goats hair embedding two or three strands of warps next to each other, rather than brown sheep wool simply wrapped around the ends). It is possible that the other kilim end wore out and was removed and that the selvages were redone at some later time. Other than that, the rug looks in very good condition.
It is wool on wool (as real tribal Beluch are).
The colours all look like they could be natural (vegetal) dyes, though I'm not totally sure about the blue, and the two or so little bits of orange could be synthetic.
The colours are also all typical Beluch colors (of the tribes that were further north, in the south you find more and different colors).
Also look at the aesthetics: toward the top right, there is one rhombus with a bright accent in the flowerhead (orange in this case). This is a choice you find in older Beluch rugs.
Again, look at how the sides of the field are irregular, with the weaver making different choices how to solve the beginning of the repeat pattern. And that the left and right are not done symmetrically. (Not also the bit of orange on the right side.) Again, compatible with older Beluch rugs.
I don't know enough to make an informed guess of the age. My uninformed guess suggests it may well be older than 1960s. Or someone followed the older examples very closely.
Old and antique Beluch rugs usually don't range among the most valuable rugs, but I've always loved the unique sense of aesthetics that goes into these rugs, and yours seems, to my inexpert eyes at least, a very nice specimen.
