Welcome Einar. As Sheryl suggests, it is often possible nowadays to find many of those old records online, which may include some of the same records your father found. And you may find things that he didn't find at the time he did his research. Just guessing here, but if your ancestors were from Iceland, you can Google 'genealogy records in Iceland' and come up with a number of places to look. My quick search, for example, showed:
and some others. If you still live in the area of your ancestors, you may be able to visit a local library or historical society and also find a lot of good sources and good advice.
If you make a reasonable effort to locate legitimate original sources and still come up empty, I personally don't think it's unreasonable, at least in some cases, to cite your father's research as your source -- especially if it's a published work and not just handwritten notes. I have, on a few occasions, used old family genealogy records as a source when I couldn't find something better. I felt comfortable with that because I had found other legitimate sources to support much of the other data in the family records, and it gave me overall confidence that it was a credible body of work.