They should be fine...but!Worm the kitten first and keep a separate litter for it for a while. You can also go to a farm store and buy the feline leukemia vaccine and administer it yourself.I give all my cats their shots(except rabies must be gotten at a vet),worm them,de-flea them, and generally just treat them with herbs. If I have to, I lance boils, shave, wipe asses,deliver kittens, cut and tie cords,induce labor, give antibiotics, etc....all my cats are healthy.And it saves me a lot on unnecessary vet bills if I can treat minor ailments at home. Diarrhea is like a big heads up for worms. Probably roundworms. If you actually see worms in the poop, chances are, it's a tape worm. They get them by ingesting fleas.