Is it possible to clone html element objects in JavaScript / JQuery?

With native JavaScript:

newelement = element.cloneNode(bool)

where the Boolean indicates whether to clone child nodes or not.

Here is the complete documentation on MDN.

Using your code you can do something like this in plain JavaScript using the cloneNode() method:

// Create a clone of element with id ddl_1:
let clone = document.querySelector('#ddl_1').cloneNode( true );

// Change the id attribute of the newly created element:
clone.setAttribute( 'id', newId );

// Append the newly created element on element p 
document.querySelector('p').appendChild( clone );

Or using jQuery clone() method (not the most efficient):

$('#ddl_1').clone().attr('id', newId).appendTo('p'); // append to where you want

Yes, you can copy children of one element and paste them into the other element:

var foo1 = jQuery('#foo1');
var foo2 = jQuery('#foo2');

foo1.html(foo2.children().clone());

Proof: http://jsfiddle.net/de9kc/