...If you copy the appropriate files from a Mavericks installation, it will work again. The files you will need to copy from Mavericks to Yosemite are:
/System/Library/QuickTimeJava to the same location
/System/Library/Java/Extensions/QTJava.zip to /System/Library/Java/JavaVirtualMachines/1.6.0.jdk/Contents/Home/lib/ext
Also download the latest version, the only change of which is to ask for Java 1.6.