There are two cat diseases that kittens are tested. Feline Leukemia (FeLV) and Feline Immunodeficiency\\irus (FIV). They are spreadthough cat to cat contact (bites, scratches, licking, etc). Now I am not sure how they are different but both have shots and are tested through bloodwork. FELV can be tested really young the FIV not till they are 3-4 months old (doesn't show up till then).
Basically, all these tests are ROUTINE for kittens. So are the shots...take the kitten to a vet and you will get everything you need.....they get different shots if they are only indoor or indoor/outdoor as well.