do NOT import gifs to Quark, especially if you are printing.
What you need to do in photoshop is create what's called a "clipping path" around the object, two pixel widths inside the object so you cut out all the white around it (I assume your image is on a white background). In your pallets, open "Paths" and click the triangle in a circle button for "new path" and draw with the pen tool (name your path "Clip" to remind you what it is.
Once you have closed the drawing (it will be a connected line in the end) then you need to make that Clip a "Clipping Path" in that same circle/triangle button on the pallett (use 2 for the tolerance) and save the file as an .eps file.
Then you can place that image in quark without the white. You may still see some white, but do a test by exporting that page to a pdf file and viewing that in Acrobat Reader, or just print the page out.
Hope that helps!