No it wouldn't pass through, because whooping cough is a bacterial infection and is fought with igG antibodies, which are not transmitted through breast milk.

Breast milk is good protecting against some pathogens, mainly those who are fought using igA antibodies.

The biggest fear I have about the anti vax movement, is that for every girl who isn't vaccinated now, and doesn't get the disease to develop immunity, means the are putting their own babies at risk in the future, because they won't be able to pass on any immunity through their placenta or breast milk when they do have their babies.