Exporting the attachments will have to be a custom piece. See an example for CRM 4.0 here, you will need to tweak it for 2011:
http://social.microsoft.com/Forums/en-US/f8aef7c4-156b-4900-87de-91bf2dae395c/downloadexport-attachments-from-dynamics-crm-40?forum=crm
next, importing the attachments can be done with some manual work using the data import wizard, as described here:
http://crmmongrel.blogspot.ca/2012/09/import-file-attachments-into-dynamics.html