OK, this makes me feel really old, but I thought it was interesting enough to pass on in case anyone else wants to give it a try.
If you (or your parents or grandparents) are still harboring children's clothes from the 1960s or earlier--the pre-wash-and-wear kind that even the Salvation Army doesn't want anymore--and don't want to just haul them off to the dump, give your state historical society a call.
That's what my Dad just did with some of our old stuff that's still lingering in their attic, and the textiles curator was interested. Not only could the clothes become historical artifacts (how scary is that?), but baby pics of us in the clothes also could become part of the collection.
I'm feeling downright historical, if not hysterical, at the thought!