Using what library (I don't see an addChild in XMLElement which seems able only to read XML, not to manipulate Dom.)

In JavaScript, I would use cloneNode method to duplicate a node.

Aha! You are right... That's NanoXML 2, to be precise.

Your method is incorrect, anyway. According to reference, new XMLElement() creates an empty element, without tag name. It is not null, otherwise addChild and getChild would throw an exception. But its toString() method, using XMLWriter manages to display null, because it is an empty shell.

When you do addChild, you put the element inside the empty element. But that doesn't make it a full, unique XML element... That's an incomplete compound (nested) element.
And I don't know this library, and the JavaDoc is quite terse, but if addChild works like JavaScript's appendChild, it actually moves the source element from its initial position to the given one.

If the source element is simple, perhaps you can clone it by doing:

XMLElement targetXMLElement = new XMLElement(sourceXMLElement.toString());

No guarantees...