Yes you can trace on to a quilt or you can transfer the drawing using transfer paper. I have done both.
To trace on a quilt, it is easiest to do by making a light box of some sort. Google how to make a light box and you will get loads of suggestions. You can even do a simple one by supporting a piece of clear plexiglass between two chairs, place a small lamp under the plexi and you have a tracing surface.
To transfer your drawing I wrote a tutorial here:
http://www.quiltingboard.com/tutoria...g-t275470.html