How can I move my database to a different domain?

First take only data dump from old domain.

mysqldump -t -n -uuser -ppassword database >  dump.sql

Then on your new domain, create database structure

mysql -u user -ppassword database < civicrm_41.mysql

(assuming you are using mysql 4.1 or above). Then import data from old domain

mysql -u user -ppassword database < dump.sql

Also be aware that in CiviCRM 1.6, the settings are stored in the database for resource paths, etc. After copying your database, you will need to go to administer CiviCRM -> Global Settings and change various paths and directories.

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