Rabbit Perch

It looks like a hat with ears in the inventory, but equipped it is a live rabbit sitting on your head, animated. The animation carries over to your marker on the minimap, and it keeps moving on a hat rack too, so it works as decoration in a build rather than only on a character.

It layers strangely with other head pieces. Several will stack on top of each other across your vanity and armor slots, and the rabbit draws over the nest the Finch Staff puts on your head instead of tucking behind it.

The Zoologist puts this on her counter before she will sell you the license for a real bunny, so you can wear one on your head a good while before you can house one. Her bestiary blurb for the town bunny jokes about exactly that, and the sprite is the fluffy Angora variant rather than the plain one.