You shouldn't really have any trouble with your tent around here, as long as it's waterproof... Buying food along the way is easy, along the Ring Road (Highway 1). There are towns every 100 km or so - or closer - and service stations scattered all around the place.
Just make sure your waterproofs are up to it, otherwise you will get wet, cold and miserable.

If there is anything you need to know, just drop me a line.

Magnus Thor
Iceland