Why do you need to export it? If you are moving from one computer to another, just copy the files. Best practice is to make sure your guest OS is shut down before backing up or copying/moving.
As far as if the feature is in the free Player or only in the Pro version, I'm not sure... The comparison chart doesn't seem to mention that. However, if it is not included in the Player version, you can always download and install the free vSphere Converter application.
