Hi Sue,
wrt ProPhoto an article by Mike may be of interest -
http://ddisoftware.com/tech/articles/december-2006-hype-or-hero-take-2-16-bit-printers/ and others.
If your printer is not 16bit, then process in Photoshop in ProPhoto, to get smoother gradients, and to capture the nuances of the 12 or 14 bits of your raw image from camera, but for printing convert to Argb (or Srgb is often just as good) would be my recommendation and print from that in Qi. You need to be careful with converting from 16bit to 8 for colours out of gamut but you can check gamut warnings within Photoshop before, or after your conversion. It depends how much you push the image around. If you let the print driver and Qi print from ProPhoto, you may not get what you expect, since I do not believe either will show out of gamut warnings. Of course, it depends on the colour range and saturation that your image contains, most often it works OK, but then sometimes it screws up real bad, and you will wonder what has happened. Of course, you should save the raw file, since you may wish to process it in some other way, or find a better raw conversion processor at some future date, but I see little point in saving large 16bit tifs today.
Best wishes,
Ray