I've been searching for something I found on the web a good while ago about the maus-slaying bunnie, and at long last I've found it. I can't sit at this machine long enough to delve further, but I offer this for what it may be worth. If valid, it doth move the tale a bit further back than labor problems.

From:

http://www.spscriptorium.com/Season4/E409secrets.htm

There are definitely two separate literary traditions at work here. According to the OED2, the earliest reference for Bunny/Rabbit Foo Foo is Chaucer's _The Canterbury Tales_, "The Knight's Tale:"
"And in the grove, at tyme and place yset, This bunnie Fewfew and this field maus be met. To chaungen gan the colour in hir face;"

The next reference is from Shakespeare, in a sonnet believed to have been written in 1609 (about the time he was hacking the Bible):
"Clear wells spring not, sweet birds sing not, Green plants bring not forth their dye. Herd stands weeping, flocks all sleeping, Nymphs back peeping fearfully, For Rabbitt Foofoo hath killed a mouse."

H.L. Mencken's _History of the American Language_, however cites a 1623 manuscript from the Plymouth colony that claims John Alden sang a "lullabye about Bunnie Foofoo" to his children.

From here, the trail disappears for several centuries. The OED2
cites a 1910 draft manuscript by B. Potter titled "Peter, Mopsy, Flopsy, and Foo-Foo Rabbit."

Back on this side of the pond, the OED2 cites a 1925 letter by Zelda Fitzgerald records that "Scott is quite upset because the publisher elided a poem about Bunny Foo-Foo from _This Side of Paradise_. Scott believed it to be essential to the narrative."

In the same year, Ernest Hemingway's journal records on 25 June (cited in Random House Hist. Dic of Amer. Slang): "Had a long argument with Joyce and Stein today. He recited some doggerel about Little Rabbit Foo-Foo. Gertrude and I recalled it as Bunny Foo-Foo. Became quite heated, and Joyce stiffed us by leaving without paying the check. Bastard."

The tentative conclusion must be that "Bunny" is the older, but changed to "Rabbit" quite early on in Britain. In America, the older form seems to have been preserved. So Americans that use Rabbit Foo-Foo are following the British tradition.
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-Mary ~:oD