You shouldn't have to use PostScript just to get layout pages; without it, type should print fine (given Adobe Type Manager) and you should see previews of images. (That is, Quark should dump the preview as RGB output.) Trying to print as CMYK would possibly also trigger an error.
I remember before I bought my first printer I was able to use my neighbor's ImageWriter (that would have been before 1993; the ImageWriter was a dot matrix printer, and my Quark version would have been about 2.0). Images, especially from Illustrator, were blocky, since they were preview dumps, but they were usable to check page layouts. You could also try Adobe PressReady, which is a software RIP (Raster Image Processer, or PostScript engine) for certain inkjet printers. See if yours is one of the ones they support; excellent results on my Epson (better than the PostScript option I bought from Epson). And not too expensive, either.
If you don't want to add a standalone RIP, you may have better luck if your images are Tiff format; eps uses encoding for the data. If you are already using Tiff, rather than EPSF format, let us know. There may be more here than meets the eye.
Hope this helps