In fact non social species, like felines, are unmoved or even aggressive toward babies not kin related to them.
But we are primates, and being primates very social, we are subject to trivers reciprocal altruism, in other words: childs are very prone to help strangers if they feeds them. They can be adopted and parassitated as muscular force in exchange of a small piece of the meal, smaller than those of the natural childs of course, as foster care studies have demonstrated. So we can find others child very attractive too, because they can be very useful to us, because they are easily exploited due to the long period of dependence from adults.
This is not directly related to the cutness, anyway, that is a physical trait, with specific characteristics (big facial elements, head bigger than the body, small arms, etc.). If one puppy develops those traits to deceive his parents, those traits will be there to be seen by all the other people too. Unless there is a specific adaptation to resist such aestetic feedback in non kin related puppies, like in some non-social species, the brain response at a cute face is the same.
Here is the final, most likely explanation for the cuteness paradox:
1 - Cuteness genes are positively selected by many things, but the main filter, at least in mammals, is THE MOTHER INVESTMENT. Puppies (humans, bunnies, all of them..) compete for the investment of the mother, because she is the one that feeds them. They cannot feed themselves until they are adults. Cuteness is a deceivement device and (because it costs physical resources) an honest signal for communicating the mother that the deceiver is the puppy most worth of the maternal investment. Even non mammals use cuteness (i.e. birds and other oviparous species) but their cuteness is rarely perceived as so because of the huge physical differences with the mammals, differences that our mammalian brain cannot see as cute but as deformities.
2 - The selective pressure is bigger when the number of puppies is greater, because the competition is more tight.
3 - Female bunnies bears more children. A litter of rabbit kits (baby rabbits) can be as small as a single kit, ranging up to 12 or 13; however there have been litters as big as 18. So the competition is harsh, and consequently the selective pressure on the cuteness genes is bigger.
4 - Women give birth to 1 or 2 children at once on average, consequently the competition and the selective pressure on cuteness genes is greatly inferior to the selective pressure on the bunnies.
5 - Assuming that cuteness is an universal estetic trait (big facial elements, head bigger than the body, small arms, etc.), developed at the same way in all mammalian brains, it is then reasonable to conclude that human babies display cuteness traits, but are not as cute as the bunnies, because those are subject to a much more tight competition.
Findings that can falsify this hypothesis:
I find the bunny cuter than any human baby I ever seen, and I believe that the majority of people will share the same feeling, but our opinions are aneddotical and do not constitute scientific proof. What we need is to take a statistically unbiased sample of people and asking who is cuter between the two, eliminating in this way the random influences (positive or negative) on the istinctive cuteness reaction caused by cultural bias or personal experiences, because those should be distributed equally and then cancelling each other, while the genetic bias should emerge as the dominant result being shared by all the people in the sample. Maybe someone will do a study about cuteness in the future, corroborating my theory or falsifing it. But the point is that there is nothing "unscientific" about evolutionary psychology. It's a science, and it's the best model of the human psychology ever developed.