Google has updated its old Favicon to the new one but even though it has been changed it is not updates or changed in firefox google search toolbar. You can do some simple step to get the new google icon in Firefox. Here is how to do it.
Get the latest Google search plugin From here .
Now replace the old google plugin with the new one for that Copy the newly downloaded google plugin(Google.xml) to C:Program FilesMozilla Firefoxsearchplugins and just replace the old one with the new.
Now press Ctrl + Shift + Del in Firefox and tick only the Cache box(you can check others as your wish) and press Clear Private Data Now button.
From now on Firefox will be updated with Google’s new Favicon.