Orders in Magento doesn't have a shipping date. They have shipments, and each one of them have a creation date.
You can access an order shipments using
$order->getShipmentsCollection();
Then on a shipment you can call getCreatedAt() to retreive creation date.
Thus, the full code will be
/** @var $order Mage_Sales_Model_Order */
foreach($order->getShipmentsCollection() as $shipment){
/** @var $shipment Mage_Sales_Model_Order_Shipment */
echo $shipment->getCreatedAt();
}