This painting is from 1865, which means you're looking at an elliptical cage crinoline like the one you lined above or there's also one in http://www.lafnmoon.com/product_p/p112.htm
(my favorite bustle/hoop pattern!). Kay Gnagey also sells them completed or in kit form.
I think fabric wise this looks like beaded and embroidered silk net (which is now prohibitively expensive - think $200+ a yard IF you can find it.) I would look for an embroidered organza instead for a similar drape. You could use chiffon as well but it will be much softer especially on that wrap she has over her arms.