Q2A consists of two parts: the web application and the database. For a migration I'd recommend the following steps:
Create a backup of your Q2A database.
Create a database (and database user) of the same name on the new (database) host.
Restore the backup to the new database.
Enable maintenance in Q2A on the source host (or configure basic auth in the web server on the destination host) to prevent other users from interacting with the site until you're ready.
Copy the Q2A application directory to the web root on the destination host.
Adjust the database settings in config.php as needed.
Enable the vhost for your Q2A site on the destination (web) server.
Log in as the admin and verify that everything is working.