did the company mention what kind of extras are included? It's not uncommon for companies to cover:
-mobile phone for personal & work use
-home internet
-money for gym membership
-subsidized lunches
You definitely want to know if there are such things covered outside of the monthly salary.
I was making a bit more than that 3 years ago in Reykjavik, living in what I'd call a loft apartment (not exactly a studio, not exactly a one bedroom, covering the whole top floor of a building) in a really nice part of postcode 107. I didn't have a car so I probably saved a lot there, but in general I was living a very comfortable lifestyle with plenty of chances to save. There is always a problem with renting in Reykjavik as inflation is generally quite bad, and many rentals are indexed. My place went up quite a bit while I lived there but generally salaries adjust as well.
What do you mean by "registration" anyway?
leiga.is is a website where you can search for rentals. In Iceland, the apartments are listed according to number of rooms, so a 1 room is a studio (bathroom is not counted as a room), and a 2 room is a one bedroom. You probably want to search for Íbúð í fjölbýli, which currently seems to be going for at least 150000 isk per month. Bland.is is another website that has rental apartments.