One of the aspects of the data reader is that it is connected to the data source while it's open. So you can't clone it in a similar fashion as you can't open a second one on the same data source.
What are you trying to achieve by cloning it? Would a better solution be to create a strongly typed object collection from the rows in the data reader? Or perhaps use a dataset which will allow for disconnected data?
-Peter
peterlanoie.blog