Simba's Cubhouse is my daughter's favorite kids club at WDW. She BEGS to go there each time we're at the AKL. I have few photos posted of Simba's in an on-line photo album (click here).
I ~think~ you can book 30 days in advance. You just use the WDW-DINE phone number. I plan on booking my daughter into Simba's for at least one of our nights during our next AKL stay (which hopefully will be very, very soon).
I booked Simba's clubhouse when I booked reservations at Jiko- 90 days in advance. You do have to give a credit card number and you have to cancel within 24 hours.
The number is 1-407-939-3463 same as dining.