As I set it back down, the seller said she'd forgotten there was no stopper, and I could have it for $5!
Still, I had no idea when this was produced, so I went to eBay. I discovered there were several up for auction, and I got a very good deal! I also discovered this is from 1971, produced by Play Pal Plastics for Walt Disney Productions. Apparently this information can be found on the back of the neck, and indeed, it appears there is some writing, but it is so shallow, it's illegible.
Barbie cleaned it up, and it came out pretty nicely. There are only a couple of permanent marks and the paint is very vibrant.
Another great find at the flea market!