Yes, Firefox is not much good if you can not launch it !

I use Ubuntu not kubuntu so I will not have the same Desktop environment as you & do not use muon. A quick web search indicates that it should install a launcher and possibly reinstalling would resolve the issue.

I found these

• Clicking on a link opens the Muon package manager to install firefox (I'm not able to launch firefox except when loading it by command line. ...)
  http://ubuntuforums.org/showthread.php?t=2141133&p=12630154#post12630154
  I solved the problem uninstalling and reinstalling Firefox through Muon.'
• How to launch Firefox browser in Kubuntu?
  http://askubuntu.com/questions/202479/how-to-launch-firefox-browser-in-kubuntu

I tried to remove and reinstall in konsole and muon. Still no go. I can open firefox I want to add it to the taskbar like as a widget. Thanks...

You may get lucky and someone answers, but you are using a Ubuntu build of Firefox and having problems with the Kubuntu desktop.

Probably it is best asking on a Kubuntu related forum how to add a laubncher for Firefox to your Desktop.

I note KDE has a variety of possible launchers and a quicklaunch widget

• https://www.kubuntuforums.net/showthread.php?59851-KDE-Application-Launchers
• From this old thread it may be as simple as dragging an icon from a list
  Create Taskbar Shortcut: How To? SOLVED http://forum.kde.org/viewtopic.php?f=67&t=88513

Thanks for the message I gather you found the quicklaunch widget. Glad to know you solved the problem