I am working on my portfolio and need to import dwgs into my Quark file layout.  Does anyone know how to do this?  Is it possible to import just the lined drawing and not the background?

 
How you have imported it. 
Try to save DWG in DXF and insert it .

If DXF did not work, save your file in eps.

eps is by far the best format to send to Quark as it is vector based and you don't lose any quality. Quark does an excellent job of rendering any eps including 32-bit color.