Welcome to Fluther.
As a European power, I would expect Iceland to have immigration, visa, employment restriction & regulation and medical licensing and permitting requirements which would be on rough par with those of the US and all of Europe (and most of the world, for that matter). Which is to say that there would probably be a lot of hoops to jump through, qualifications to meet and prove and regulations to follow that aren’t always intuitively obvious and clear. That would apply in spades when you’re dealing with a field as specialized as medicine.
However, just as Icelanders need the same type of medical care that all humans need from time to time, they also need other semi-related types of help that may not be so highly regulated and licensed, and which might be suitable for you.
For example, well-off families may want nannies and other such caretakers for children. There are probably opportunities for some nursing in that line. Likewise, private nurses can nearly always find a place, if they can meet the sometimes demanding and are flexible to handle the not-always-by-the-book requirements of the patient / customer. I expect that Iceland’s relatively large fishing fleet (relative to the total population, that is), may impose some demands for at-sea medical care that would not rise to the level of having doctors on board trawlers. But if you’re willing to learn the fishing trade (and put up with the physical demands and privations required), then that might make you more valuable in that way when your competence in medical matters is required.
So it’s going to take some research and work on your part to see how you can fit in and what you can start to do as you progress toward what you would ultimately like to do. I doubt if anyone can walk up to an Icelandic Consulate and request “the form to emigrate to Iceland and work as a nurse practictioner” then just walk in and start work.