Create your profile in code and dynaically add required add-ons.
Let's assume that you saved Firebug XPI into the C:\FF_Profile folder as firebug.xpi (go to Firebug download page, right-click on the "Add To Firefox" and save as C:\FF_Profile\firebug.xpi).
Below is the code:
final String firebugPath = "C:\\FF_Profile\\firebug.xpi";
FirefoxProfile profile = new FirefoxProfile();
// Add more if needed
WebDriver driver = new FirefoxDriver(profile);