I agree with Manfred's posts.
A red warning flag went up when you posted that you don't have your driving license yet. I need to add a bit to what Manfred wrote about driving there. First, I have been driving for many years, and I spend a lot of time in mountains, etc., but I have rarely encountered roads as frightening as some in Iceland. The main roads are fine, and drivers behave themselves. However, things deteriorate quickly. Many roads are very rough dirt roads, and many have no guard rails. For example, here is one in the NW fjords area, south of Isafjordur:
It's even worse than it looks, because the volcanic rock is friable, and pieces just fall away. Not far from where I took this picture, a piece of the road had simply fallen off into the ocean. And this was a road that had been repaired not long before. So if you are a new driver, some of the secondary roads will be quite dangerous.
I asked an Icelander with whom I went kayaking the fjords whether people often drive off the roads. He said that it is seasonal. If I recall, he said that it was OK in the winter because people are more careful, but I may have it backwards.
Second, once you get away from the southwest, there can be very few people, so if something goes wrong, you can be stuck for some time. My son and I were on the road in this photo for hours and saw only two other vehicles. The drivers of both stopped when they saw us and gave us the traditional (if maybe revealing) Icelandic greeting: "Are you OK?"
However, leaving driving aside, it is an amazing place, and the hard thing is figuring out which parts to see in whatever time you have.
Re Manfred's comment about the redheads--there has been a lot of genetic study of Icelanders because of their isolation (until recently) and their superb data. The museum in Rejkjavik had an exhibit about this when I was there. Genetic studies confirmed that the Vikings took captured Celtic women with them.
One last thought: be prepared for bad weather. It can happen any time.