It sounds like a nice project.
You can get really fancy and have the 6 lights do related things like a pumpkin-chaser or one fades while one brightens.
Reading your code, it seems like that will give you a bunch of random flickers. This will be a lot harder to code, but you can have the randomizer choose a target value and then have it more gradually fade towards the target (doing this concurrently for 6 values will be a bit tricky to program, but using hardware PWM and interrupts will help a lot).
int ledPins[LEDCOUNT] = {3, 5, 6, 9, 10, 11};
randomSeed(analogRead(ledPins[0])); // a little trick for getting more
This will work just fine, but just to be clear you're doing the analog read on a different pin than the LED is actually on the LED is on digital pin 3, you're reading from analog pin 3. I think it only adds some confusion, and will cause problems if you try to analogRead(ledPins[4]);. Better to use analogReead(2); or some such.