I dont' know anyone who's renting places in what seems like your target price range who goes through an agency. Almost all the rental properties in Iceland are privately owned- there isn't really such thing there as entire apartment blocks owned by a a management company that rents them out.
You sometimes have to have some months rent as a security deposit up front, but there won't be some kind of council tax or anything extra. Utilities are additional but might be included in some rentals. In the 8 years I lived in Iceland, I only paid utilities separately in one apartment.
Given that the rentals are usually done directly with the owner, the flexibility and willingness to rent to someone who's not in Iceland or with Icelandic ID can vary greatly. I've lived in places that varied from the strictest max upfront deposit, Icelandic rental contract, 3 months notice if you leave the apartment to one with no deposit, verbal contract, and a month's notice (granted, from someone I knew well already).
If you're looking to fly by the seat of your pants, it might be easier if you move late summer/early fall when the craziness of summer rentals is over. Anyone who wants to make a buck tries to rent out to tourists over the summer months.
One final note: you say you're looking at 2015. Icelanders are not generally huge advance planners so you'll probably have a hard time securing something anytime soon. Also, inflation is crazy bad there so prices you see now are likely to be quite different by then. For example, a place that I rented in 2009 cost 90000isk then is now going for 140000isk.
Surviving Iceland
