Hi Lany,
Found this from one of the CIC website's FAQ.
I'm pregnant. Can I wait until after I give birth to take the medical exam?
No, you are still required to undergo a medical examination even if you are pregnant. However, certain parts of the examination may be postponed until after you give birth. You should discuss your options with the Designated Medical Practitioner examining you.
http://www.canadainternational.gc.ca/uae-eau/visas/medical-medicaux.aspx#pregI guess this will also apply to your cousin.