Not sure about doing it in Quark, but you could open it in PaintShop Pro and save it as a gif, setting the background as transparent. Then import it back into Quark.
Create your transparent file in photoshop and save it as a eps file, beware the onscreen quality will be rubbish, but when you print it will be as good as an original. Not sure gif will offer you "print" quality, eps will.
For images in quark you can use the clipping feature to transparantize an image.