Now, I'm almost out of my stash. At least I had the foresight to cut a bit of the selvedge off with the name of the manufacturer on it. It didn't take long to track it down, and then to find an online store that carried it. Unfortunately, the selvedge didn't have the name of the color on it.
The fabric is by Timeless Treasures Fabrics, Inc., and is part of their "Complexion Collection." The pattern number is km-c7966, and the color I've been using is "Cameo" (I think), though I see it comes in several shades that would be nice for dolls. I just bought six yards from this store (no affiliation, just one of the first links on Google when I did a search): http://www.hingeleyroadquilting.com/search.aspx?find=complexion+collection
June 26: I just got an email from doll-friend Susan Saint-Leaves. She told me the above link no longer has the cameo colored fabric pictured here, which actually appears a little darker than my stuffed dolls. I think the dolls may appear lighter partially due to the white stuffing used, or maybe I bought a different color at the Fabric Depot. I'll compare when my new order arrives - I got their last 4 7/8 yards. I'd really like to get my hands on samples of all the colors.