Plan to cure that hangover with a few more of what got you there? “Hair of the dog” shortens “hair of the dog that bit you,” since early medical theory held that a bite wound (including the rabies it may have caused) could be treated by rubbing into it some hair of the biting animal.
You’re “barking up the wrong tree” if you are misdirected in your efforts. This comes from the habit of hunting dogs to stand at the base of whatever tree the hunted animal escaped up and bark to indicate its location. When the dogs are mistaken about which tree the prey is in, they are literally “barking up the wrong tree.”
The idea that a dog year is equal to 7 human years seems to derive from the idea that dogs live about 10 years and humans live about 70. Happily, human life expectancy in the developed world is now a good bit older than 70, and dogs do not all “age” at the same rate, with smaller dogs typically living much longer than very large ones.