Are you using Maildir storage with IMAP? If so, it should possible to just move the messages into the new folders. It should also be possible to use a mail client to copy between the two IMAP folders.
It is important the the messages have a Date header, as this is usually the preferred date. Some clients will prefer the Delivery-date instead. If all else fails, they may used the date the message appeared in the folder. As long the messages have a Date header, then the dates should remain the same.
Emailing between the two servers will reinject the messages into the mail stream and result in the Date headers being replaced.
EDIT: My experience with Dovecot and Thuderbird indicates that as long as the Date headers exist, the date doesn't change when a file is moved using IMAP. If the Date headers are absent, then the date is set to the date the file shows up in Thunderbird. IMap internal date value is specified in RFC-3501 Internet Message Access Protocol section 2.3.3. Based on my reading of the RFC, I would expect the Delivery-date header to be the significant header.
If you are moving files using IMap, Postfix is irrelevant as it is not involved. Postfix will only be involved if the messages are being mailed between servers.