I do think that kittens would most often be named the cutest, though. And btw, I thought of posting this poll after seeing your Kitten: "I meant to do that!" OP.
I'd guess kittens and puppies would dominate any such poll, partly because they are favorite pets and so many of us grew up enjoying their cuteness and antics.
But I've noticed for years that kitten calendars will usually be sold out before puppy calendars, and cat memes seem to be more popular than dog memes online. I believe there are about as many dog lovers as cat lovers. But I have noticed, with quite a few dog lovers I know, that they really favor specific breeds, or at the least specific sizes of dogs, and aren't nearly as fond of different types of dogs. (That isn't true of all of them, but I know it is true of some, including some in my own family.) OTOH, cats and kittens, compared to dogs and puppies, are closer to one standard, not drastically modified by breeding over centuries. So a kitten calendar will probably appeal to more cat lovers than a puppy calendar will to dog lovers. And a dog lover who prefers only certain breeds or one particular size of dog might think those particular puppies are the cutest life forms ever, but kittens are cuter than drastically different breeds/sizes of puppies.
I also googled the very important question of kittens and cuteness, and ran across this Guardian article:
https://www.theguardian.com/commentisfree/2018/apr/11/cats-why-are-kittens-so-cute