There is plenty of cool gear and gadgets that you can tote with you that will make running with your dog fun and convenient. For water and treats, you can bring along collapsible bowls or drawstring bowls that will have attachments that work great with hands-free leashes that have D-rings or sturdy clips.
Consider investing in a good harness that will put less strain on your dog than a collar and will provide more comfort or even saddlebag storage. For those going to more extreme places, there are even padded “shoes” for dogs that will protect from more rough terrain.