Zimbra 7.0.0 (currently in beta3) has an export-import features for account and password from Exchange, Zimbra or general IMAP Server, but if you wish to do similar task on Zimbra 5 or 6, following article may help :
Script for Export-Import Zimbra Mail Server Account & Password
The above script will export Zimbra account, password, sn, givenName, displayName and so on (modify script for another field on Zimbra LDAP) and create 2 files : a zmp and ldif file. zmp for import account and ldif for modify password on the destination to be similar with the original server.
Note : if you use Ubuntu/Debian, remove ! symbol on top line of script, so it will looks as below :