The first example on this page is also a bit verbose. Since the DomElement class inherits/extends the DomNode class, one does not, in fact, have to get another reference to the first node. The create_element method has already given you that reference. (Also, the last line passes a string to the append_child method, instead of a DomNode object) Simplified:
<?
$new_element = $dom->create_element("new_element");
$new_element->append_child($another_element);
$oldTag->append_child($new_element);
?>