Follow the following..
Backup in full: Open Source Edition Backup Procedure - Zimbra :: Wiki
* Double check that it really backuped up everything
Upgarde from OSS to NE:
1) Get Zimbra Network Edition license
2) Download the Zimbra Network Edition installation file.
The version you download must the same or a newer version of Zimbra and for the same operating system.
3) Copy your Zimbra license to /opt/zimbra/conf
4) Perform the Zimbra upgrade process. its as simple as runnig the new install packge ./install.sh
Zimbra will then be upgraded from Open Source to the Network Edition.
if case of problem..either rollback to your backup or ask Q here
Raj