Wilderness SP headquarters is 9.7 miles from the center of Mackinaw City, or say about 10 miles from the ferry docks. I'm not sure exactly where the new loop is in relation to park headquarters (or to the older camping loops either).
Arnold line still allows dogs on board; I don't know about the others. It sounds as though there are more services for pets on the Island than there used to be, too:
http://www.arnoldline.com/other-links/faq I think Arnold still has the traditional ships rather than hydrofoils.
Mmmm . . . I'm thinking of pasties . . .