One such start-up is called Rover, which is a website that connects pet owners with pet sitters. It's easy to use: Go online, find a dog sitter and book a reservation. There are now 25,000 sitters available across the U.S. The company says business booms during the holidays.
"During the holidays, people travel on Thanksgiving and on Christmas," says Aaron Easterly, Rover's CEO. "So there is a wave of people looking to book all the same days. It's a crazy time of year for us."
Rover makes money by taking a 15 percent commission from its sitters, who typically charge $30 per night. The company claims a nearly 600 percent year-over-year jump in revenue growth. Venture capitalists have piled in. Menlo Ventures, for instance, invested $12 million in the start-up.
"The logic is simple," says Venky Ganesan of Menlo Ventures. "Leaving your dog in a kennel is like leaving your kid in an orphanage. The kennel industry is a $5 billion market today but we think, with Rover's help, it could be a $30 billion market."
Read MoreAirbnb valued at $13B ahead of staff stock sale
Rover isn't the only player in this market. Rivals include DogVacay, which has 20,000 dog sitters. The start-up has already raised $47 million from investors. Benchmark's Bill Gurley sits on the company's board.
There are critics of these start-ups, however. Laura Laaman is president of Outstanding Pet Care, a Connecticut-based consultant to pet care facilities. Laaman said pet sitters pose a potential safety risk.
Read MoreA liability risk for Airbnb hosts
"Just because you have a pet doesn't mean you're qualified to care for another person's pet," Laaman said.
Rover's Easterly counters that every sitter on his site is verified and reviewed, and that dropping off your dog with a sitter beats leaving him in a kennel.