First of all, DO by default wont have anything installed.. No panel, no software.. Do gives you barebone VPS meaning, via their panel you can deploy only a clean OS installation !!
On top of the OS now, its your job is you install the software (like web server, email server, DNS manager, FTP server, etc). A panel, like cPanel or DirectAdmin is a paid software, which comes with all these (what is needed to run a website and web applications) along with a GUI based easy to work web panel.
Yes you can very easily install cPanel in DO.
As per cPanel.net (cPanel creators) you may need 2GB or more RAM with clean installation of CentOS 6 or above. cPanel is a paid software, so you have to pay cPanel.net or any of its re-seller for license to use it, which is around USD 15 a month of USD 200 a year I guess..
That is it, once you get it installed, for which you may follow the guide of cPanel.net documentation, you may proceed towards website transfer from old host to this new server of yours.
For reference, you may read,
VPS Deployment -> https://www.digitalocean.com/community/tutorials/how-to-install-cpanel-on-a-virtual-server-running-centos-6
cPanel Installation - > https://www.digitalocean.com/community/tutorials/how-to-install-cpanel-on-a-virtual-server-running-centos-6
cPanel is a convenient application that allows users to administer servers through a GUI interface instead of the traditional command line. Although the installation for cPanel is relatively simple, the script does take several hours to run. Here's how to install cPanel on a virtual server running Centos 6