Whooping cough is caused by a bacterium called Bordetella pertussis. The bacterium infects the lining of the airways, mainly the windpipe (trachea) and the two airways that branch off from it to the lungs (the bronchi). The symptoms of whooping cough usually take between six to twenty days to appear after infection with the bordetella pertussis bacterium. This delay is known as the incubation period.

Reference:
http://www.cdc.gov/pertussis/about/causes-transmission.html

Laboratory diagnosis: It include culturing of nasopharyngeal swabs on Bordet-Gengou medium

Polymerase chain reaction (PCR): The polymerase chain reaction (PCR) is a biochemical technology inmolecular biology to amplify a single or a few copies of a piece of DNA across several orders of magnitude, generating thousands to millions of copies of a particular DNA sequence.

Serological methods: The bacteria can be recovered from the patient only during the first three weeks of illness, rendering culture and Direct Fluorescent Antibody (DFA) testing useless after this period, although PCR may have some limited usefulness for an additional three weeks.

Reference:
http://www.nhs.uk/Conditions/Whooping-cough/Pages/Diagnosis.aspx