I'm guessing these doll eyes came from a prized doll that had great sentimental value to the person--or parent of the person--who managed to have them removed from the doll and mounted on this little stand, which I imagine was custom made for the purpose! It appears that the eyes are made of metal, painted, by hand I believe, and the armature on which they are mounted looks to be copper. The bottom end of the mount has been bent inside of a steel U-shaped base, with a tiny piece of cardboard I believe stuck inside to keep everything tightly upright. (Indeed, it is very stable.) The eyes themselves, which I have shot here with some magnification, still have some blonde eyelashes attached!
I found this piece at a fantastic antique shop in Hew Hampshire filled with extraordinary things, and think they make for quite the extraordinary little curiosity! The piece measures 2 1/8" tall x 2" wide x 3/4" deep. There is some wear and cracking to the paint (more visible here in magnified views than with the naked eye) and some rust on the base, but good condition overall and not as fragile as they appear.