I have found only one occurrence of the U.S. phrase can a moose crochet?.
Hodges & Hines: Swing’s Our Thing is an album by the U.S. jazz saxophonist Cornelius ‘Johnny’ Hodges (1907-1970) and the U.S. jazz pianist Earl ‘Fatha’ Hines (1903-1983). Recorded at Coast Recorders Inc., San Francisco, California, on 13th and 14th November 1967, this album was released in 1968 by Verve Records under the reference V6/8732.
This is what the British jazz historian Stanley Frank Dance (1910-1999) explained in the sleeve notes of this album:
The program consists of originals and standards in the proportion Johnny Hodges usually favors. He himself came up with three new headshaking, footpatting pieces: Open Ears, Bustin’ with Buster, and what is by all odds the most arresting title in years, Can a Moose Crochet? The peculiar humor of this folk phrase, used as an emphatic negative, appealed to Johnny when he heard it out West.
According to A Dictionary of Catch Phrases British and American, from the Sixteenth Century to the Present Day (Taylor & Francis, 2005), by Eric Partridge and Paul Beale, the “emphatic negative” phrase can a moose crochet? means well, hardly or no, that’s impossible.
Hodges & Hines: Swing’s Our Thing (1968): album cover—photograph Discogs: