Close, but not close enough. There will be clone()an element in the code below , then add it to #panel.
jQuery(document).ready(function()
{
jQuery('#button').clone().appendTo('#panel');
});
Please note that this is not up to standards to IDbe used twice on the same page. So, to fix this:
jQuery(document).ready(function()
{
jQuery('#button').clone().attr('id', 'newbutton').appendTo('#panel');
});