We cannot use plugins on wp.com. They are bits of code you can add to wp.org self hosted sites that do various things beyond the basic design of the template. Here we can use widgets and shortcodes to do quite a few of the things plugins will do.
You could decide to self-host, but you would be responsible for paying a host, buying a name, and maintaining and fixing whatever goes wrong with your site.
Here is the difference between different sorts of wordpress:
By the way, domain mapping would mean you still have a wp.com blog: it is just sort of a roadsign pointing your domain name to your blog. People see the domain name, but you are still using wp.com as a host with its restrictions.
What sort of code does your plugin have? What exactly do you want it to do? Perhaps there is a work-around.