“A hosue is not a home without a dog” is a saying that has been printed on many gift items, such as signs, plaques and mugs. The saying has been cited in print since at least 1968.
 
 
30 March 1968, Chicago (IL) Tribune, “In the Wake of the News” by David Condon, sec. 2, pg. 1:
Nonetheless, this was a dog, and a house is not a home without a dog.
 
24 April 1968, Christian Science Monitor, “Duchess and her nine puppies take over” by Darren Stone, pg. 14: ‎
There is a saying that a house is not a home without a dog.
 
20 May 1972, The Daily Mail (Hagerstown, MD), “Main Street” by Dave Cottingham, sec. 2, pg. 1, col. 2:
Both families enjoy living with antiques; both feel that a house is not a home without a dog.
 
5 May 1974, Press-Register (Mobile, AL), “They’re Home Safe!” by Elizabeth Park, pg. 11-D, col. 2:
People adopt pets for many reasons, running the gamut from the desire to give a pet as a present to someone else to the feeling that “our house is just not a home without a dog.”
   
Google Books
Scarlett O’Hara’s Younger Sister:
My lively life in and out of Hollywood
By Evelyn Keyes
Secaucus, NJ: L. Stuart
1977
Pg. 251:
Our captain had said during one of our talks that a house is not a home without a dog.
 
Google Books
House of Havoc:
How to Make- And Keep- A Beautiful Home Despite Cheap Spouses, messy Kids, and Other Difficult Roomates
By Marni Jameson
Cambridge, MA: Da Capo/Lifelong Books
2010
Pg. 217:
According to the Humane Society, I’ve got lots of canine-loving company: 39 percent of U.S. households own at least one dog, and 75 million dogs are pets. Yes, many are trouble. However, I’m sure the two-legged residents of those 39 percent households would agree with me: A house is not a home without a dog—or two.