It is offered on Tuesday and Sat. AM's for the concierge guests at AKL only. They meet you in the lounge at around 7AM (I forget the exact time) and they take you to AK...for a short tour of some of the backstage areas, then you board one of the Kilamanjaro Safari vehicles (this is well before the park opens) and they take you out on the safari trail to animal watch...the safari ride takes maybe 30 or 45 minutes...great views and LOTS of animal activity. Then they take you back to Tuskers for a special breakfast buffet in the private dining room. The food was AWESOME, and they have the Safari guides and an African woman from Tuskers stay with the group while you eat to visit and answer questions. Children are welcome and I think group size is limited to 30 people. It is well worth the cost IMHO if you are staying in an AKL concierge room.
If you are interested in the Sunset safari but need something to do with children, you might check out the various childrens programs at the Deluxe resorts.... my kids always thought it was a big treat to get to have an evening at one of them when the grownups had their night out. We used the ones at Beach Club, Poly, WL and GF on various trips and they loved every one of them. BC and GF were their favorites (and they seemed like they had the fewest things to do, but the girls loved both of them). It was one of the things they "couldn't wait" to do on each trip... we would plan 1 night out each trip and they loved it.