Watching Dark Crystal got lions pondering if such a dog creature could be realized as a sphere robot covered in fur.  It could have an actuated mouth & eyes.  The movie creature got around both by slowly walking on 2 tiny legs & by rolling to go fast.  The legs could be used for jumping.

Still at a loss for any practical use.  It probably would be a windfall as a mass produced AI toy.  The fur would have to be a removable sock, which would make eyes, mouth, nose, & legs difficult.  Everyone wanted a hacky sack 40 years ago.  A fur sack that rolled via single paw controller could be a souped up hacky sack.  Another thing everyone had was a furry pencil eraser.

A rolling fur ball wouldn't last long.  A durable fur robot definitely needs feet.  There were efforts in 3D printed fur, before all investment shifted to AI.  The closest thing to structural hair might be 3D printed snakes.

https://thangs.com/designer/ruvenbals

 There is a collection of sliding mechanisms which resemble large scale hairs.  The motion would have to be rotational instead of linear.

Stylized spaghetti hairs made of TPE might be durable.  This could be a practical application of sideways printing, a 1mm nozzle.

It could roll on standoffs on the top side of the fur while the feet extended on the bottom side.

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For all the dreams of a practical replica of the movie prop's motion & modern humanoid hype, physics dictate a conventional 3 wheeled base with an actuated muppet on top.  There are very low quality replicas of the fur ball under fizzgig search terms.