Firebug is not officially compatible with Firefox 6 since as of this writing, Firefox 6 is on early alphas. However, forcing compatibility works with it. For that, just install Nightly Tester Tools addon and in Tools>Nightly Tester Tools, check “Force Addon Compatibility” and restart Firefox. Now, you will be able to install and use Firebug.
Firefox 6 alpha 1 nightly has been available for quite a while now. You can download and install it on Fedora and other RPM based distros from the Firefox Nightly page. Search for the latest rpm and download it and then install it by double clicking on the RPM. To launch it, go to Internet menu and launch “Nightly”.