"The Rabbit" is a poem by Lord Alfred Douglas, first published in the June 10, 1896 issue of a weekly called The Sketch (No. 176, vol. XIV, p. 264). The poem was reprinted in an 1898 collection called Tails with a Twist. This is the version in the 1928 edition of the complete poems of Lord Alfred Douglas:
THE RABBIT
The Rabbit has an evil mind,
Although he looks so good and kind.
His life is a complete disgrace,
Although he has so soft a face.
I hardly like to let you know
How far his wickedness will go.
Enough, if this poor rhyme declares
His fearful cruelty to hares.
He does his very best to keep
These gentle animals from sleep,
By joining in with noisy throngs
Of rabbits singing ribald songs.
To wake their fears and make them bound,
He simulates the Basset-hound.
And if he meets them after dark,
He imitates the greyhound's bark.
Douglas, Alfred Bruce. "The Rabbit." 1896. The Complete Poems of Lord Alfred Douglas, including the Light Verse. London: Martin Seckere, 1928. p. 154. Accessed at hathitrust.org 28 January 2024
Though this has many similarities with the lines Hastings quotes, it is not an exact match. A closer version appears in 1909 in the Wisconsin Medical Journal, of all places. A report on a dairy show mentions the poem in passing:
What Wallace Irwin said about rabbits might with a slight stretch of the imagination have been applied to much of the milk that formerly reached the market:
"The rabbit has a pleasant face, its private life is a disgrace, I really cannot tell to you the dreadful things that rabbits do."
"The National Dairy Show." Part of the "Editorial Comment" section of Wisconsin Medical Journal, vol. VIII (June 1909–May 1910), No. 5, October 1909. pp. 265–266. Excerpt is from p. 266. Accessed at archive.org 28 January 2024.
This opens up the possibility that Wallace Irwin wrote a better known variant of Douglas's poem. However, the poem is not easily found in Irwin's works online.
In the 1920s, the second edition of the popular anthology The Week-end Book includes a version attributed to that prolific scribbler, "Anon., 20th Cent.":
THE RABBIT
The rabbit has a charming face:
Its private life is a disgrace.
I really dare not name to you
The awful things that rabbits do;
Things that your paper never prints—
You only mention them in hints.
They have such lost, degraded souls
No wonder they inhabit holes;
When such depravity is found
It only can live underground.
Mendel, Vera, and Francis Meynell, gen. eds. The Week-end Book. 1924. 2nd Ed. Enlarged and Revised, 1925. London: Nonesuch Press, 1926. p. 171. Accessed at archive.org 5 April 2024.
Like the snippet in the Wisconsin Medical Journal, this version varies considerably from Douglas's poem, but is close to what Captain Hastings says. As it postdates "The Market Basing Mystery," The Week-end Book cannot be Christie's source, but a version of this sort is evidently the one she has in mind.
Later in the decade, Anne Carroll Moore edited The Three Owls, a series of three volumes on children's literature. The second volume contains an essay by Marjorie Williams Bianco in which she mentions "that well-known rhyme beginning:"
The rabbit has a pleasant face;
His private life is a disgrace.
Williams Bianco, Marjorie. "Easter Rabbits—and Others." The Three Owls: Second Book. Contemporary Criticism of Children's Books. Written and Edited by Anne Carroll Moore. New York: Coward-McCann, 1928. pp. 249–254. Accessed at archive.org 28 January 2024. Passage quoted is on p. 252.
Since this too postdates the publication of the short story, it is possible that Williams Bianco is quoting Christie. However, she calls it a "well-known rhyme." It therefore appears more likely that this poem about leporine depredations circulated in the oral tradition in several different forms the 1920s and earlier, with Douglas, Irwin, the editors of The Week-end Book, Williams Bianco, and Christie all contributing different versions or passing along existing ones.