8.75 months - Kili vs. 4 week old kittens

I am fostering 5 kittens for the local Humane Society. They came to live with me when they were about 4 weeks old. Kili is obsessed with the little critters. She just so desperately wants to play with them and is somewhat distraught that I will not allow it. Pretty cute. Many of you know how important it is to me for my dogs to be small animal safe since I own several rabbits. I agonized and worried about Kili and whether raising a puppy with critters would truly result in a dog that was safe. I wondered whether it was possible for a dog to just be born with such a high prey drive that it couldn't be brought up to be safe. I do still wonder if that is possible, however clearly I do not need to worry about Kili.