Keep in mind that if you've got a pack on, there's no reason your dog shouldn't as well.

I've yet to backpack with my dogs, but I've done plenty of long day hikes with them. They have no problem carrying their gear, food and water on their own backs.

Of course, they're also very well trained, very in-shape dogs. If you're going to take a dog on a backpacking trip, start with long walks about the house, and build up to long day-hikes, before putting in a multi-day trek.