Firstly we are assigning divs into variables (optional)
var firstDivContent = document.getElementById('mydiv1');
var secondDivContent = document.getElementById('mydiv2');
Now just assign mydiv1's content to mydiv2.
secondDivContent.innerHTML = firstDivContent.innerHTML;
DEMO
http://jsfiddle.net/GCn8j/
COMPLETE CODE
<html>
<head>
<script type="text/javascript">
function copyDiv(){
var firstDivContent = document.getElementById('mydiv1');
var secondDivContent = document.getElementById('mydiv2');
secondDivContent.innerHTML = firstDivContent.innerHTML;
}
</script>
</head>
<body onload="copyDiv();">
<div id="mydiv1">
<div id="div1">
</div>
<div id="div2">
</div>
</div>
<div id="mydiv2">
</div>
</body>
</html>
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