I live in SW Iceland and have often photographed the aurora. I have the DA 12-24 f4 and the DA* 16-50 f2.8. I most often end up using the DA 12-12 f4 because 16mm is too narrow, and the aperture difference doesn't matter as much. The aurora often covers a good portion of the sky and moves while you're exposing, so the wider the better.
Iceland in March isn't very cold, but can be quite wet and windy. I second Professor Batty's recomendation for a fleece sweater and windbreaker. I also often wear rain proof trousers and gloves, and bring along mittens over the gloves just in case. I'd also recommend renting a four wheel drive vehicle, although they're probably more expensive. This allows you to drive to better vantage points without getting stuck in the mud.
I'm a bit worried about the route you'll take between Stykkisholmur and Fludir, as the most direct route will probably be impassable in March, and you will probably have to go through Reykjavik. You might want to look at the map at
http://http://www.vegagerdin.is/english/road-conditions-and-weather/the-enti.../island1e.html to see which roads are closed. This map is updated frequently and is generally a good guide to driving conditions here.
Thrainn