Hi Amanda, one of my sons was a huge Lion King fan too!
You can often see Rafiki and Timone near the front entrance of Animal Kingdom Park. When you arrive at the Park, stop by Guest Relations and pick up a copy of the Show Times Guide. It will tell you where and when you can see which characters that day. If you are looking to find a particular character, you can ask them for that information on the day you are visiting (it's subject to change daily).
During the dates that you are there, the
Festival of the Lion King show will be at 10am, 11am, noon, 1:30pm, 2:30pm, 3:30pm and 4:30pm daily. In addition, on October 8th during Extra Magic Hours, there will be a 6:00pm showing.
Hope this helps and have a wonderful vacation with your family,
Kaylene