Java is not installed by default in OS X 10.7 and later.
Java cannot be easily removed, once installed.
To determine if you have Java, launch Java Preferences from Applications > Utilities, and you'll either get the preferences display, or a dialog indicating that the Java run-time will need to be downloaded and installed, and you can choose to skip that (and leave Java off the system) or install the Java run-time.
The Java web plug-in will also be disabled if it's not used often enough, again to reduce the risk to system security.
If this is a shared OS X system and isn't a dedicated computer, then consider allowing or consider requiring your child to use another computer for games and such; Java has been a recent and common target for security attacks, it's had vulnerabilities including the recent Flashback attacks. Further, kids have occasionally been known to install stuff that they probably should not have, and that's occasionally led to issues arising for other users sharing the system.