So as Andre wrote - subclass QNetworkCookieJar, make the two protected functions public and use them to transfer the cookie data. No need for a copy constructor as far as I see. Left alone that a copy constructor would do quite the same.
Or implement a cloneFromOther Method to simulate an assignment operator/copy constructor:
void MyCookieJar::cloneFromOther(const QNetworkCookieJar *other)
As mentioned before, QNetworkCookieJar is a QObject and there simply IS NO copy constructor. It does not help to ask again and again - the trolls will not add it :-)