Hi, you likely do need to upgrade, yet it's probably not possible.
Open Java Preferences in Applications>Utilities>Java, do you see these versions...
So we know more about it...
At the Apple Icon at top left>About this Mac, then click on More Info, then click on Hardware> and report this upto but not including the Serial#...
Model Name: eMac
Model Identifier: PowerMac6,4
Processor Name: PowerPC G4 (1.2)
Processor Speed: 1.42 GHz
Number Of CPUs: 1
L2 Cache (per CPU): 512 KB
Memory: 2 GB
Bus Speed: 167 MHz
Boot ROM Version: 4.9.2f1
Thanks, Since we're dependant on Apple dor our Java updates, you're as far as you can go on Java on your Mac, sorry.
Though if you still find tht Mini useful, upgrading it to 1 GB of RAM can speed it up significantly...