Try downloading the Firebird installer and using that to install Firebird instead of using the zipped version. This should add the registry settings. After you run the installer, you'll have to run the Sun Java installer again for it to detect the Firebird installation. This should also make installing other plugins easier as well. It worked for me when I tried Firebird (I went back to Mozilla for now).
Microsoft does have it's own version of Java, but many programs, especially cross-platform ones like Mozilla/Firebird use Sun's Java version as it is also cross-platform.
goates