Magento : Check if customer Page

you can add check with getModuleName

<?php $modulename = Mage::app()->getRequest()->getModuleName();

if($modulename=="customer" && Mage::getSingleton('customer/session')->isLoggedIn())
{

}?>

You can try below code, for customer dashboard links below handler is alwasy there, so you can check below handler

if(in_array('customer_account',$this->getLayout()->getUpdate()->getHandles())){
  // your code 
}