While not the oldest quilt design, the (generally agreed upon) oldest quilt still in existence is the The Tristan quilt dating from 1360 - 1400 in Italy. Here's an interesting (and brief) article about the history of quilts:
http://www.historyofquilts.com/ancient.html
Also Barbara Brackman's blog is a wealth of information on the historical aspects of the craft.
http://barbarabrackman.blogspot.com/