In 1741, a retired Dutch sea captain named Douwe Mout van der Meer transported the first live rhinoceros to continental Europe since 1579 to Rotterdam. He called this amazing beast Clara, and the two of them traveled the continent nonstop for the next 17 years; a contemporary map of their journeys, with its colourful arrows and sinuous lines, looks like something out of the back of an in-flight magazine.

Such ramblings were worth the work for Van der Meer (it took eight horses to pull Clara's cage). His rhino became well-known very quickly. People were prepared to pay the equivalent of half a day's work for the pleasure of her company — despite her diet of hay, bread, orange peel, and the odd draught of beer, her demeanor was always serene.

That skin with the armour plating! The solitary horn that gave her a unicorn-like appearance in the eyes of the general population! Clara's presence was a smash with the people, but she was also a popular with the artists, who immortalized her in marble, bronze, porcelain, pencil, chalk, and oil - and due to this, she'll be able to relive the experience all over again.

The Barber Institute of Fine Arts in Birmingham has owned a tiny bronze of this extraordinary pachyderm (A Rhinoceros, called Miss Clara, c1750, after Peter-Anton von Verschaffelt) since 1942, and it's around this adorable sculpture – stubby but determinedly proud – that the gallery has built its latest exhibition, one that includes not only many artistic representations of Van der Meer's rhinoceros, but also depictions of several other celebrity beasts, The end effect, a genuine zoo of a presentation, is almost perfect.

This is the nicest tiny exhibition I've seen in years, curated by the Barber's head of collections, Robert Wenley: a single-room presentation that fills the viewer with awe at every turn.

The first depictions of Clara date from 1749, and include a pair of anatomical engravings by Jan Wandelaar for Professor Bernhard Siegfried Albinus's treatise Tabulae Sceleti et Musculorum Corporis Humani, in which she appears next to a human skeleton; apparently, Albinus thought the animal's "rareness" was a "agreeable" ornament in context.

But, if she's a little out of the frame now — munching the cud serenely, Clara seems blissfully unaware of the rattling bones nearby - she'll be front and center from now on. When she visited Augsburg in Germany on June 12, 1748, Johann Elias Ridinger, a German artist, drew six sketches of her, and now you can see her "personality" – or one of them – starting to form.

In one, she's shown as an ancient crone, her eyes rheumy and her skin wizened; all she needs is a hat to complete the effect. Both images contrast with Jean-Baptiste Oudry's c1749) Study for the 'Dutch' Rhinoceros, in which she appears battle-ready, with a breast-plate of skin slung around her middle, and even more so with Pietro Longhi's oil, The Exhibition of a Rhinoceros at Venice (c1751), in which her appearance is almost velvety, the sable folds of her hide loose and luxuriant.

A tiny throng watches Longhi's painting, signaling a subtle change in the exhibition's tone. Humans, with the exception of skeletons, have not intruded until now, and the mind now hesitantly turns to concerns of freedom and captivity.

In the 18th and early 19th centuries, Europeans had little knowledge of how to care for the exotic animals they coveted. Even the creatures' environments were difficult to conceive for most people: when rhinos are shown in a landscape in this exhibition, it's usually surreal, a mishmash of palm trees and dock leaves.

Of course, this did not deter the menagerie keepers. Destruction of the Furious Elephant at Exeter 'Change, 1826 by George Cruikshank depicts the sad demise of Chunee, an Asian elephant who went "mad" and threatened to break out of his pen at Edward Cross's menagerie in the Strand, where he'd been a resident since 1814 (he was killed by a firing squad, an outrage that sent "elephant-struck" London half-mad with grief).

This collection of animals, which included a camel and many kangaroos, was later known as Polito's Royal Menagerie, and it occupied the upper floors of a retail arcade — and it was rather renowned, even if it did include a "hippopotamus" that was really a tapir. Lord Byron wrote in his journal in 1813 that "the Ursine sloth hath the very voice and manner of my valet," and that the pre-madness Chunee behaved so nicely that he wanted him to be his butler.

One of the most intriguing objects in the collection is Rudolph Ackermann's aquatint of the Exeter 'Change menagerie from 1812, with the animals arranged as if in a department shop and the stylishly dressed visitors staring at them hungrily, as if they may be for sale. Of course, it's heartbreaking: the animals have little place to move.

The feeling of being hemmed in is oppressive. (Reading about the transition away from amateur menageries and sideshows, as well as the pressure, not least from the public, that led to the founding of the Zoological Society of London, is reassuring.) Curiosity and excitement abound, as does the impression of a vast universe yet to be explored. The crowd's goggled-eyed delight makes you almost envy.

But maybe there's no need to be envious. I must confess that I was a youngster again in the clutches of this quietly stunning display. It's simply so enjoyable. By no means is Joseph Wolf's watercolour (c1850/51) of Obaysch, an Egyptian hippopotamus who caused a sensation when he arrived in London, with thousands flocking to see him at the zoological gardens, the best work of art in the show (that honor may go to Rembrandt's 1638 etching of Adam and Eve, in which an elephant stands for goodness in the face of the trickster serpent).

But it was the animal designed to seem so sleek, with a face as gentle as an old parson's, that I felt most strongly pulled to. I was struck with what I can only describe as utter ecstasy when I read about Obaysch's "unctuous appetite for dates, his jog-trot manner of going" on the train home while eating an unsatisfactory sandwich. What a world it is that has (almost) such animals in it.

Thanks to Rachel Cooke at The Guardian whose reporting provided the original basis for this story.