Before I tell you how I made it, let me start by saying that this bauble isn't a real quality item. It may not even outlive the trend. But once I found the toy animal (on the cheap, by the way) I didn't want to go out an buy a bunch of other supplies, so I made use of stuff I already had on hand. If you want, you can too.
First, cut the head off of a perfectly good toy with a box-cutter. You know, with the blade facing away from you and all that. Then throw on a few coats of craft paint and trace the outline of the opening at the back of the neck onto a yogurt lid (or some other flat piece of plastic that you'll be able to cut out with scissors). Cut it out.
Shove a pin through the plastic, and gob lots of hot glue around the pin head to keep it in place. To add some sturdiness, position the pin so that it's pointing downwards a bit.
Do some paint touch-ups if you need to, and then put her in the wall or on a cork board. Don't hang heavy stuff on it. It won't hold. Think necklaces and ribbons. Or nothing at all--just let it be there in all its gloriousness (like taxidermy, but less queasy-making)
If you want something sturdier, I would imagine that filling the head with cement and sticking a screw in it (pointy side out) would be a good way to go. Spray paint would probably outlast bottled craft paint. If I ever decide I need more of these babies, I'd get the proper supplies and take the time to do a good job of it. But this mickey mouse job works just fine for hanging my measuring tapes. And I didn't have to change out of my pajamas to go to the store.