You might want to call them. One of the canoe liverys allow them with a doggy life jacket. I see them on the little miani alot.
I've lived around the canoe rental area for over 11 years. I cannot say with absolute certainty, but in all that time, I've never seen a dog in a canoe, not have I seen one in the vans/school buses they use to transport customers to launch sites. Liability I would assume. You personally have to sign off on a waiver that you won't hold livery responsibility for injuries you suffer while using their canoes. Pets don't have that opportunity.
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