What Ira suggests is by far the easiest thing to do. Your Quark document (in landscape view - that is, lying across the screen rather than upright) will have two pages, but each one is divided in two, so that the first page of the Quark document has Layout Page 4 on the left and Layout Page 1 on the right.
The second page of the Quark document has Layout Page 2 on the left and Layout Page 3 on the right - exactly as you would expect to see those two in use. Note that since 2 and 3 are a spread-to-view, you could run a picture across from one to the other, though you wouldn't sensibly be able to do that with 4 and 1. Also, if your layout design has a margin around the edge of each page, then on 2 and 3 you would have two margins seen next to each other down the centre, which you may consider to be too much margin. In that case increase the width of your 2-and-3 layouts towards the centre line so that you end up with only one normal-width-worth of margin down the centre.
Finally, the Quark text box linking tool will happily run text from 1 to 2 and 3 and then back to 4 again if need be.
Paul Sanderson, London UK