check for libjavaplugin.so in Mozilla/firefox with the url: about:plugins

In a terminal:

$ locate libjavaplugin.so

You may need to manually add a symbolic link to libjavaplugin.so in:

/usr/lib/mozilla/plugins

or

/usr/lib/mozilla-firefox/plugins

or

/usr/lib/firefox/plugins

or

whatever

After you find out were the installer put the plugin and where your firefox
plugin directory is. I or someone else will show you how to make the
symbolic link.

I am running Dapper at the office and am not using the same version of java
you are.