The Baluchistan pygmy jerboa exists (and is widely described as "very cute.")
A widely-circulated photo purporting to be of the "world's cutest rodent."
On 18 February 2016, the web site The Cutest published an article about the "world's smallest & cutest rodent," also known as the Baluchistan pygmy jerboa. While the article did describe a real (and very cute) animal, also known as the Dwarf Three-Toed Jerboa, the lead image in that particular article featured a felt doll:
While we have not been able to determine the exact origins of the above-displayed image, it has been featured in several Pinterest collection of "realistic felt animals" and featured in a gallery of felt creations on the web site of a company called Heidifeathers. The photo is typically accompanied by a description of how the doll was created:
Needle felted pigmy jerboa. This felted pigmy jerboa is carefully and detailedly made even tiny fingers and fine whiskers. Using wire, soft wool and plastic eyes. This is about 2 pound coin size ( 500yen coin ), same size as actual pigmy jerboa.
While the above image does not show a real animal, the article on The Cutest accurately reports that the real Baluchistan pygmy jerboa was named the smallest rodent in the world by the Guinness Book of World Records in 2010:
The Baluchistan pygmy jerboa, or the dwarf three-toed jerboa is the only species in the genus Salpingotulus. Adults average only 4.4 cm (1.7 in) in head and body length, with the tail averaging 8 cm (3.1 in). Adult females weigh 3.75 g (0.132 oz).
A video shows the actual pygmy jerboa, which looks quite a lot like its felted counterpart: