Margery Fee & Janice McAlpine, Oxford Guide to Canadian English Usage, second edition (2007) has this entry on Canadian use of "have got to":
have got to Commentators have condemned the use of have got to meaning be compelled to, recommending must or have to instead: that is, 'I must (or have to) go' rather than 'I have got to go'. However, Webster's Dictionary of English Usage notes that Otto Jesperson collected many examples of have got to from a range of important British writers, among them Dickens, Trollope, and Shaw, and its authors ad a list of their own that includes William Faulkner and several American presidents. In other words, it is not necessary to avoid have got to.
This assessment of "have got to" basically gives the wording a green light. But two other elements of the sentence "Say, have we gotta have any coupons for chicken or rabbits?" remain to be explored: the use of "gotta" for "got to," and the use of have as the infinitive at the end of a phrase that also begins with have.
The contracted form gotta is sufficiently informal that Merriam-Webster's Eleventh Collegiate Dictionary (2003) declines to provide an entry for it. The American Heritage Dictionary of the English Language, fifth edition (2010), however, steps up with this entry:
gotta Informal Contraction of got to: I gotta go home.
The form gotta owes its existence to attempts by writers to approximate the pronunciation of "got to" used by many native English speakers in North America (and perhaps elsewhere). But clearly the word doesn't raise any grammatical problems that "got to" does not.
As for the second have in "have we gotta have," it may sound odd in this construction, but it is present in many declarative (as opposed to interrogative) constructions of the same basic syntactical form such as "you've gotta have a license" and "I've gotta have something to eat." And the awkwardness of "have we gotta have" is hardly improved by swapping in "have to" for "have got to" in the quotation: "Say, have we to have any coupons for chicken or rabbits?" (Even "Say, must we have any coupons for chicken or rabbits?" sounds a bit weird, owing partly to the mismatch in register between "Say" [in the sense of "Hey, wait a minute"] and "must we" [in a sentence position where "do we have to" would be the most likely choice in informal spoken North American English] and partly to the clunkiness of "must" and "any" in the sentence; once must enters the picture, some seems a better modifier than any for coupons, although the sentence would sound even more natural without any modifier: "Must we have coupons for chicken or rabbits?")
If I were composing the quoted sentence, and I chose to start it with "Say" and to include "gotta" part of the way through it, I would be strongly tempted to replace the first "have" with "do," to maintain the speaker's diction at a consistent level:
"Say, do we gotta have any coupons for chicken or rabbits?"
But the author may have blanched at the prospect of having even a character prone to using informal speech patterns and forms say "do we got to."
If, on the other hand, I didn't want the speaker to sound indifferent to educated syntactical norms, I would probably have worded the sentence this way:
"Say, do we need to have coupons for chicken or rabbits?"
But the author's version of the quotation is grammatically and syntactically defensible—and it is certainly possible that someone—Canadian or not—might actually say those words rather than the ones I would have chosen.