What is interesting about your code is that I just tried to run it and a got errors. So I could not test it. For this reason, I tried another way:
$adapter = new Zend_Http_Client_Adapter_Curl();
$adapter->setCurlOption(CURLOPT_REFERER, 'http://www.google.com');
$client = new Zend_Http_Client('http://www.example.com');
$client->setAdapter($adapter);
$client->request('POST');
var_dump($client->getLastRequest());
The above code results in:
string 'GET /domains/example/ HTTP/1.1
Accept: */*
Referer: http://www.google.com <-- THE REFERER
Host: www.iana.org
Connection: close
Accept-encoding: gzip, deflate
User-Agent: Zend_Http_Client
' (length=180)
So in this case it seems Referer header is set correctly.
EDIT:
On the OP's request I also tested:
$adapter = new Zend_Http_Client_Adapter_Curl();
$client = new Zend_Http_Client('http://www.example.com');
$client->setAdapter($adapter);
$client->getAdapter()->setCurlOption(CURLOPT_REFERER, 'http://www.google.com');
// This line below results in error:
// $client->getAdapter()->setCurlOption('referer', 'http://www.google.com');
$client->request('POST');
var_dump($client->getLastRequest());
This also works as before.