That's exactly The Rabbit that came to mind and made me really want one as The Doctor or Companion (Not the Regular Series, an Unboiund Audioplay or Webisode...)
I know there's Frobisher, but, he's not that Rabbit. Though Iris Wildthyme's Companion Panda is fun
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?