You cannot natively copy most of the internal classes, but you might want to look in to IExternalizable (http://www.adobe.com/livedocs/flash/9.0/ActionScriptLangRefV3/flash/utils/IExternalizable.html)
It is the method of serialising objects used internally by AMF. It forces your objects to create two methods, readExternal and writeExternal. The idea is that writeExternal allows you to package up the objects internal state in a ByteArray, then a new instance of your class is created, and AMF will pass that ByteArray in to the readExternal method, where you can recreate the previous objects internal state by hand. The calling of the methods and instantiation is all done for you through the ObjectUtil.copy() method (http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/mx/utils/ObjectUtil.html?filter_flex=4.1&filter_flashplayer=10.1&filter_air=2#copy()) if you're using the Flex SDK, otherwise, the copy implementation is as follows:
function copy(value:*):*{
var buffer:ByteArray = new ByteArray();
buffer.writeObject(value);
buffer.position = 0;
var result:Object = buffer.readObject();
return result;
}
As you can see here, it's only the readObject and writeObject methods of ByteArray that actually do the serialisation, there is no real need for the ObjectUtil class.
You may also need to register a class alias for the class you want to copy so AMF knows what object to create, otherwise you will just get generic Objects out the other end:
registerClassAlias("com.example.ExampleClass", com.example.ExampleClass);
It should be noted that you cannot have required parameters in the Constructor of objects you wish to copy by this method, and that ByteArray's readObject will check the object to see if it implements IExternalizable, otherwise it will just copy its public properties. This is why most of the built in classes will fail to copy.
On the point of copying Graphics from within Display Objects, there are a few methods you could use:
As of FP 10, Graphics has another useful method.
public function copyFrom(sourceGraphics:Graphics):void
(http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/flash/display/Graphics.html#copyFrom())
So once you've copied your Object, you can then manually copy the graphics over. Just put this in to the copy() method. Just check to see if it extends Sprite or MovieClip and then call copyFrom(). This would be the easiest to write.
And here is another new method.
public function drawGraphicsData(graphicsData:Vector.<IGraphicsData>):void
(http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/flash/display/Graphics.html#drawGraphicsData())
If you were to store all the commands as raw data (even JSON them, or create internal DTOs), then write the IExternalizable methods to copy the commands over to the new Object and repopulate the Graphics using this method. This would be a pain to write, but would mean you just call the copy() method and you have a copy, Graphics and all, without any custom code in the copy() method. You could also call the graphics methods dynamically based on the commands, so you could get this to work in FP9 if required. This has the added bonus of allowing you to change the commands as that's not currently possible. Once you write to graphics, you're stuck with it.