Anime: Wata no Kuni Hoshi

Yes, she's actually a cat.
Wata no Kuni Hoshi (Star Of Cottonland) is a 1978 shoujo manga and 1984 anime film.

Chibi-Neko is not a human girl with cat ears and a tail. She's a normal kitten, but she wants to be human and imagines herself as such. She is never shown as a cat, only as a toddler girl with long beautiful hair and a frilly dress. And cat ears and a tail.

The story is about her adoption into a human family and her struggles with her identity as a cat. If you don't want anything that deep, it's also a Ridiculously Cute Critter story. Think of Chi's Sweet Home with a big dollop of surreality.

It contains examples of: