cPanel does not have Docker by default. If you have root access to machine which runs cPanel of course you can install it but you will not be able to control it via cPanel.
You can check these cPanel support pages:
https://support.cpanel.net/hc/en-us/articles/360062418794-Can-I-run-docker-on-a-cPanel-server-
https://support.cpanel.net/hc/en-us/articles/4402393047703-How-To-Install-Docker-Compose-
And I think you don't have root access to that shared machine. Therefore I think you are just looking for a way to publish your Laravel application on a shared hosting.
A basic Laravel application needs it's files on a server and a database connection (if needed). cPanel can provide both of this. You can upload your Laravel application files to your cPanel Website users home folder, arrange directory structure and point that Website's HTTP requests to your application's public
folder.
You can use cPanel's File Manager or connect your server with a FTP client to upload and rearrange your application's files.
An application needs a database connection. In cPanel you can create a MySQL database and a MySQL user for it. Then you can change your database connection settings according to them.
You can check some other StackOverflow answers and tutorials for "Publising Laravel on a cPanel shared hosting"
How do I upload a laravel project on cPanel shared hosting?
https://medium.com/@kajan746/how-to-host-laravel-project-on-cpanel-83389d6d31e6
But as I said before; this has nothing with Docker. Those instructions shows how to use file manager and mysql wizards to prepare a production environment for Laravel on a shared cPanel host.