I'm not sure about dogs but I know parrots and other birds are DNA tested quite regularly. My grey has been tested and I got the kit to test our macaw but havent' had the heart to collect even the few drops of blood needed but it is VERY reasonably priced for parrots. The basic tests and testing to see if it is male or female, testing for 2 diseases is only $35.
here's a link for one site that does the canine testing.
http://www.vetdnacenter.com/fees.html
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"Anybody who doesn't know what soap tastes like never washed a dog."
The most affectionate creature in the world is a wet dog