Is it Cotton (I don't think so)? Silk (seems more like rayon)? A Wool Challis?
Really eye-catching setting using a Log Cabin block as the center medallion of a quilt. The fabrics have me a bit stumped though.
Links to more on wool challis:
http://crystalamesbury.blogspot.com/2010/07/fabba-reeque.html
http://www.museumoflondonprints.com/image/138408/printed-wool-challis-dress-1838
http://www.bensilver.com/gbb-woolchallis.dlp
http://www.stellarubinantiques.com/items/499041/enlargement499041sra.html
http://www.bing.com/images/search?q=Wool+Challis+Fabric&Form=IQFRDR
http://www.bing.com/images/search?q=Wool+Challis&qpvt=Wool+Challis&FORM=IGRE