OP, your plan sounds like lots of fun, and I have always wanted to do a long backpacking trip, or training across Europe, and kept telling myself I would do it summer before med school...until I realized all of the things everyone else on here is telling you.
May I suggest planning a mini backpacking trip for this summer, then saving the long trip for either summer after med school (though honestly there will probably be some obligation that you need to attend to instead during this time, especially if you need research, etc for a competitive speciality), or after school/residency?
My parents hiked the Appalachian Trail after they finished residency, taking a full 6 months off before starting their careers. Just a thought.