Well, I'm not sure what I'd call it, but…
I think I'd start with the body and fur of a cat, a small, maybe kitten-sized (once it reaches adulthood), cat. Independent most of the time, but affectionate and part of the family too. A lot of the quirky personality of a cat too. But the cat part of this animal won't like to lick cardboard or mail I accidentally left on the floor while I'm trying to sleep, and it won't attempt to act like an alarm clock like my cat does in the morning when he feels that I should be awake. It will cuddle with me while I sleep when it's cold outside and while I read or watch TV.
Then add in a bird, something with brightly colored feathers like a parrot or a parakeet, but a song like a nightingale, so it will have a musical purr. No harsh or annoying noises, just a pretty bird call. And wings that are mostly just for show and the cuteness factor, but that it can glide through the air on if it jumps off something.
And for added fluffiness, an angora rabbit. I could make wool from its fur and make a sweater decorated with shed feathers from its wings.
Well, maybe not. ^_^ But it would be small, fluffy, cuddly, and it could glide off the sofa to the floor.