If you were moving to another hosting provider or to another account within the same hosting company, then yes:
1 - Backup the database and the site files;
2 - Restore them on your new account;
3 - Change the web.config connection string to match your new database;
4 - Add the new domain to the PortalAlias table;
But according to your description, you were not moving the site, just changing the domain.
Cheers,
Aderson