Section 14.18 of the HTTP standard deals with the circumstances under which we must or must not send a Date header. For almost everything a normal mod_perl user does, a Date header needs to be generated. But the mod_perl programmer doesn't have to worry about this header, since the Apache server guarantees that it is always sent.
In http_protocol.c, the Date header is set according to $r->request_time. A mod_perl script can read, but not change, $r->request_time.