It wouldn't be a kitty idiom [1] for nothing, right? Although we know plenty of pets that fight like cats and dogs [2], a recent study at Tel Aviv University found that two-thirds of the 200 polled pet parents to both reported a positive relationship between the species!
Turns out age is much more than a number – If your pets are introduced when less than six months for kittens and a year for dogs, they could easily become fast friends according to a statement from Joseph Terkel [3] of the school's department of zoology:

This is the first time anyone has done scientific research on pets living in the same home. It's especially relevant to the one-third of Americans who own a pet and are thinking about adopting a second one of the opposite species.

Do you think cats and dogs can be BFF [4] or at least squabble-free roomies?

Source [5]