I'd recommend something like this:
Take a snapshot of the filesystem and database(s) and get the current site running on the new host and new domain name. See: https://docs.civicrm.org/sysadmin/en/latest/misc/switch-servers/
Upgrade the filesystem to Drupal 7 (updating the CiviCRM package to CiviCRM 4.1.6 for Drupal 7 in the process of this upgrade so it is ...
I have not used a QNAP for this, but have in other contexts. You might be able to install entware ( https://www.qnapclub.eu/en/qpkg/556 ) and use that to install php7.1 or similar QPKG from entware's repo