i wouldn't say it's a bad idea but there'd be lots of things you'd have to think about first.
you'd have to build the dog up before the tour so it'd be fit enough to handle it, and even then, be aware of how fast you're travelling and how many miles you're covering per day.
i'm reading a book, 'Across the Great Canadian Wilderness' at the moment. it's about two guys who trek across Canada. they take a dog with them. i'm not sure if it survives yet but it's already had some pretty tough experiences, and they're only in Saskatchewan! (going from West to East).