Hi Kevin,
2 up in the interior is going to be tough in places, but I guess it is possible if you choose your routes. The pillion will need to walk some sections of sand, rivers and hills. The Iceland Overland book has good descriptions of routes and what is possible with which bike. For example it will tell you there is lots of deep sand or big rocks, and warn against taking heavy bikes on some routes. Be prepared to turn back if the risk is too high, I would say don’t ride anything you can’t ride back over. That might sound bollocks but I have learnt the hard way, many times over the years.
Having said that, Iceland has lots to offer on the main routes so I might suggest you stay on the main roads with a pillion, you will not be bored that’s for sure. Route 1 which follows the coast around Iceland is mostly sealed, 99 percent of the rest is dirt. I found the North West had spectacular roads and scenery.
The only thing I took which I did not need was a water filter. I am going to chuck the bloody filter, it's the second trip I have taken this on and never used, it must have done 25000 miles. I carried 5 litres of water and that was good for two days, if I couldn’t find any water everybody was happy to give me some if I asked. I think it is good to be self sufficient in terms of tent and cooking as there are so many opportunities for wilderness camping. If you use a GPS I can share some waypoints. I used Garmin / Mapsource world map.

Steve