There was no doll just a small white book with a zipper that the names were placed in at least in the temple I was in your experience may have been different.
At least when I was there in 1983 and 1984, I believe it was a white, satin, zippered pouch. I watched a temple worker putting little slips of paper in there with names for the prayer roll.
I could ask a current temple worker who works there every Friday to see if she's every heard of anything like that.