You can describe your kitten as your young feline friend, since feline describes anything having to do with cats.
The adjective feline is useful when you're talking about cats — just as canine describes dogs, and ursine describes bears. You might talk about the special feline food and toys you buy for your pet, or describe his feline beauty. You can even describe a person as feline, if something about him or her is catlike. The Latin root felinus means "of or belonging to a cat," from feles, "cat."