Migrating from Gmail to Google Apps
Solution 1:
Premiere Edition accounts comes with an Email Migration tool that does just what you asked for (but don't use the POP3 protocol because it won't preserve your labels).
It won't migrate your contacts though, to do that you need to export them for your current account, then import them in your new Google App account.
Solution 2:
Since you've got a premier account you should be able to just use imap to connect to the gmail servers from the email migration tool. This should preserve the labels since they're just stored as imap folders (double check this first though). It won't migrate the contacts or filters though, that'll need doing manually, I don't believe anybody has created anything to automate doing that for you.
See also this question
Solution 3:
Thank you for taking the time to try and resolve my issue. I finally had Google Support look into the issue.
They had to change a couple of settings in order for the Migration to start working again.
- They changed the host to : imap.googlemail.com (instead of imap.gmail.com)
- They dropped the number of connection to 3 (insetad of 5)
Once again, I really appreciate everyone's feedback on this.