dog whisperer
n. A person who has, or claims to have, a natural ability to relate to or connect with dogs.
Madcap mutts and frantic Fidos will be cured the caring way when one of the world's few 'dog whisperers' comes to Gloucester on Sunday. Steve Fryer, a one-time stable manager for the Emir of Bahrain, has become something of a celebrity because of his uncanny affinity with dogs.
—“Dog whisperer in visit,” The Gloucester Citizen, November 01, 2001
1998 (earliest)
The dog whisperer, Marianne Miner has a special relationship with Almond, her affectionate, personable guide dog.
—Jeff Houck, “The Pet Whisperers,” The Palm Beach Post, May 15, 1998
This phrase is, of course, a direct descendant of horse whisperer, a phrase popularized by The Horse Whisperer book and movie. As you might imagine, there are many kinds of "whisperers" in the world besides the horse and dog varieties. There are cat whisperers, bird whisperers, rat whisperers, mouse whisperers, elephant whisperers, snake whisperers, and even iguana whisperers. In fact, it's probably true that there's a whisperer or three for every type of animal you can name.

Returning to the canine version, a book called The Dog Whisperer was released in September 1999, but the earliest citation only goes back to the previous year.

In case you're wondering, horse whisperer started showing up in print in late 1994 when Disney bought the film rights to Nicholas Evans' unpublished novel.