Over in Facebook, Cliff Johnson has unearthed this wonderful ad, which he posted under the title “Cocked”:
It’s genuine: from Vol. 22 Issue 2 (December 1918) of Little Folks Magazine, on a page (96) of ads for Christmas toys, all of them gun-related.
“Big Dick” heads the page, which also has the Premier Repeating Pistol (a cap gun); Shoot! (a shooting game, involving tenpins and a repeating cannon that shoots wooden plugs); the Daisy Liquid Pistol (a water gun); the Daisy Air Rifle; the Daisy Military Pop Gun; and a “regular cowboy holster”.
Clearly the slang term dick ‘penis’ had not yet made its way into common use in 1918; Dick was still just a nickname for Richard. OED2 has dick ‘penis’ (marked as coarse) from J. S. Farmer’s compendium Slang in 1891; then in a dialect quotation (Dost turn thysen to t’wall, lad, so’s us ‘ns sha’n't see tha dick?) in 1929; and then from Henry Miller in 1934, by which time it was clearly widespread slang.
Big Dick seems to have been a common collocation, due to its phonological satisfactions; and big dick is certainly a common collocation now, for the same reason.
On Little Folks, from a wiki for Salem MA:
Little Folks Magazine was a young person’s magazine published in Salem from 1914-1928.
Margherita Osborne was its editor.
Her obituary was published on July 11, 1954.
Little Folks started publishing in 1897, but in Salem from 1914-1928. The editor was Margherita Cassino Osborne, daughter of Samuel Edson Cassino. Her father was a naturalist and his other publications were all science related. Margherita managed all of the Salem publishing operations with her second husband Frank Wellman Osborne, according to the Streets of Salem blog.
(The reference to “the front” in the ad is to the Great War, what we now know as World War I. When this issue of Little Folks went to press, the Great War was presumably still going on; the Armistice was signed on November 11, 1918.)