Well, this exists. It's the Dogbrella, a combo of a dog leash and an umbrella, and it is pretty amazing.

See, dogs just can't handle the rain! So in order to protect them from that dastardly water, you can just hold this ridiculous thing over your pooch. The attached chain will make sure they stay under its protective shield. And your other hand will presumably be free to hold an umbrella for yourself. Unless you need that hand to carry your doggie's treats, because it doesn't matter if you get wet as long as your precious pooch is taken care of.

Hammacher Schlemmer via Geekosystem