Well, the weather in Iceland in late August, early September, is pretty similar to the weather in other similarly situated countries (i.e. close to the ocean in the northern part of the tempearate zone) - think Ireland minus a few degrees. Unless you live in a desert (which you might actually do - if you don't have ANY water-resistant pants) you should be fine with what you've already got.
It is of course difficult to give clothing advice without the slightest indication of what you hope to do in Iceland ...
As for Icelandc rain, it's all subjective. It rains often, yes, but torrential downpours are almost unknown, it just drizzles. The wind does whoever do quite well at driving the drizzle into your face ...