This is from the well known trekker Andrew Skurka, who did an East/West traverse that would cross similar terrain to your proposed route:.
Question:
I have asked around and everywhere I hear that water is sufficiently available in all areas, but I keep wondering about this ‘desert’ area that you also talk about. The area around Askja seems so dry and empty to me and running out of water there seems to be one of the worst things to do. So how was your experience on this?
Andrew's reply:
There’s plenty of water. You might have to carry some, but never much. Plus, you don’t burn through much water in those cool, windy conditions, hiking on flat terrain.