If you want to do everything in one week, you should go in June when when you have sun and light almost all night long so you can take advantage of late travelling hours to gain time. We traveled in a rhythm 9AM - 12AM, thus approx 15h per day. Also you need to take into account that you will stop a lot and all the time for pictures as everything is so incredible.
The map shows you our route and you can check it out also in google per day, just click in the left corner up on the icon next to Iceland to see the details.
For a more clear overview below also a graphic of the trip.
We had in total 3088km traveled. We rented a 4WD as for some roads it is hard to access with a 2WD. It of course also depends on the weather, for example for Snaefsjokull National Park as it had not rained for some days it was safe to go with a 2WD.
You can of course read more on the Europe - Iceland tab about my trip around Iceland