A reminder: you will need Java installed in order to play Minecraft. Either the "legacy" Java 6 that Apple provides or Java 7 from Oracle. Java does not have to be usable by a web browser for Minecraft to work, and I strongly recommend that you turn Java off for your web browser as it is a popular way for malware to get onto computers. If you must use Java in your web browser for reasons other than Minecraft, at least use Java 7 as it is more actively updated than Java 6, which is pretty much at end of life for support.
FYI, I run Java 6 and do not have it available to any web browser. Minecraft works fine in it.