There are two dates available in the order: The date of the creation of the order, and the date of the latest modification of the order.
The date of shipping is not known.
If you want to manually enter the date of shipping for each order, you can create a custom field of the table "order" and of the type "date" via the menu Display>Custom fields, with the Business edition.
Then, you can use such code:
<?php echo JText::_('DATE').': '.$this->element->CUSTOM_FIELD; ?><br/>
where CUSTOM_FIELD is the column name of the custom field.