pup nup
n. A prenuptial agreement that specifies who gets custody of the couple's dog or dogs.
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Etymology
Examples
2014
One of the more common things Mr Edward sees is people fighting over pets.

“I’ve coined the terms pet nup and pup nup.

“It should say if the couple bust up, John gets the poodle or the wife gets the parrot.”
—Kylie Adoranti, “Casey, Mornington Peninsula, Frankston and Brimbank have the highest number of divorcees in Melbourne, ABS figures show,” Melbourne Leader (Melbourne, Australia), September 23, 2014
2013
When considering a prenuptial agreement, couples usually include their thoughts on pre-marital finances, 401K plans, bank accounts and real estate. But they should also discuss what to do about dogs, cats and other animals acquired before and during the marriage.
—Gina Calogero, “Prenups and Pup-Nups: Getting it in Writing,” Gina Calogero Attorney at Law, February 15, 2013
2008 (earliest)
Most important, keep refocusing on the dog during all the turmoil. Now more than ever, dogs need routine and clarity….And if you ever dare slip a ring on your finger again, consider the wave of the future: "pupnups."
—Denise Flaim, “When marriage goes to the dogs, who gets them?,” Newsday, May 15, 2008
Notes
The general term pet nup dates to mid-2011. The feline variation cat nup is surprisingly rare, probably because, in the event of a divorce, it's the cat that decides who gets custody.