This cat may be harboring rabies that will be discovered up to 11 months from now, in one rare case 6 years. The typical incubation period for rabies runs 21 to 240 days. Hence, the usual legal 6-month (183 day) quarantine for possible rabies infections in any animals -- that duration is just beyond the peak of this incubation-range curve. A 6-month quarantine is still not safe, it's just "safer". Keep in mind too that giving a wild-harvested cat a rabies-shot does not cure it of rabies if it already has rabies -- nor are rabies-vaccines at all effective on the undeveloped immune systems of kittens. A cat or kitten may or may not show any symptoms of harboring rabies up to the point of its death. Not all animals exhibit the so-called "furious rabies" symptoms during the 2 weeks before death from rabies. 1 out of 5 (~20%) of all rabid animals only exhibit minor symptoms of lethargy, paralysis, or disorientation; called "dumb rabies" or "paralytic rabies".
Thanks to TNR practices and free-roaming cats you are now four times more likely to contract rabies from any cat than any other domesticated animal. This is why even the CDC has issued direct warnings against the use of those failed TNR (trap, neuter, re-abandon) programs anywhere and everywhere: http://onlinelibrary.wiley.com/doi/10.1111/zph.12070/abstract
That being said, rabies may be just one of your problems now.
These are just the diseases these invasive species vermin cats have been spreading to humans, not counting the ones they spread to all wildlife. There are no vaccines against many of these, and are in-fact listed as bio-terrorism agents. They include: Afipia felis, Anthrax, Bartonella (Rochalimaea) henselae (Cat-Scratch Disease), Bergeyella (Weeksella) zoohelcum, Campylobacter Infection, Chlamydia psittaci (feline strain), Cowpox, Coxiella burnetti Infection (Q fever), Cryptosporidium Infection, Cutaneous larva migrans, Dermatophytosis, Dipylidium Infection (tapeworm), Hookworm Infection, Leptospira Infection, Giardia, Neisseria canis, Pasteurella multocida, Plague, Poxvirus, Rabies, Rickettsia felis, Ringworm, Salmonella Infection (including the most dangerous new super-strain found only in cats), Scabies, Sporothrix schenckii (Sporotrichosis), Toxocara Infection, Toxoplasmosis, Trichinosis, Visceral larva migrans, Yersinia pseudotuberculosis. [Centers for Disease Control, July 2010] Bird-flu (H1N1, H5N1, H7N2), Bovine Tuberculosis, Sarcosporidiosis, Flea-borne Typhus, Tularemia, Rat-Bite Fever, SARS, an antibiotic-resistant strain of Staph aureus (MRSA -- Meticillin-Resistant Staph aureus) "The flesh-eating disease", and Leishmania infantum; can now also be added to CDC's list.
Yes, "The Black Death" (the plague) is alive and well today and being spread by people's cats this time around. Many people have already died from cat-transmitted plague in the USA; all three forms of it transmitted by cats -- septicemic, bubonic, and pneumonic. For a fun read, one of hundreds of cases, Cat-Transmitted Fatal Pneumonic Plague -- http://www.ncbi.nlm.nih.gov/pubmed/8059908
"Recommendations to avoid zoonotic transmission:
Cats are considered the most important domestic animal involved in plague transmission to humans, and in endemic areas, outdoor cats may transmit the infection to their owners or to persons caring for sick cats (veterinarians and veterinary nurses)."