We've had to move it several times now. The general procedure is:

* install apache2-worker and mod perl
* create the stats user on the new box
* copy the awstats, data, and scripts directories
* copy the cron jobs
* copy the /etc/apache2 default-server file
* copy the /etc/sshd files
* copy the stats/.ssh
* copy the root/.ssh
* copy the root cron scripts and entries