If you didn't install it, you don't have it, But you can check
Open Terminal and paste/type
and press enter
if you do have it, turn it off in your web browsers preferences.
Yes uncheck Java so it's not enabled, check Javascipt on so it is enabled, and yes download the Apple Software update.
The malware folks are ahead of Apple as always.
Am I fundamentally disabling Java for future use? Is this ok?
No, you can enable Java if you need it but it's hardly used, use it only on sites you trust.