I have found out that Firebug for Firefox is an open source project and we can extend it.
By searching for documentaion about Firebug extension development I found the following website:
http://www.softwareishard.com/blog/extending-firebug/
Unfortunately its petty old and doesn't have information for current versions (i.e. 2.0.x) of Firebug.
My goal is to extend Firebug's inspector feature.
So can anyone please tell where I can find an up-to-date guide for Firebug extension development?
The existing Firebug 2 is broken once e10s is enabled by default in Firefox. That's why Firebug 3 (aka Firebug.next) was recreated from scratch based on the built-in devtools.
Therefore it is recommended to base new developer extensions on the built-in devtools instead of the old Firebug 2 source.
A guide describing how to do that is available at the Mozilla Developer Network (MDN). And there are also example extensions in the Firebug repository on GitHub as well as a template extension created by one of the devtools developers.