Z Nation (2014)

S1E1 Puppies and Kittens

Three years into the zombie apocalypse, a mismatched group of ordinary individuals bands together to escort the sole known survivor of the zombie virus from Upstate New York to a laboratory in California, aiming to use his blood to develop a vaccine. They encounter an unexpected challenge in the form of a zombie baby, and unbeknownst to them, their final chance for a vaccine harbors a sinister secret that could endanger them all.