Animal Kingdom is my 5 year old's (and also 12 year old's) favorite park.
As others said, do not rush. Take your time and explore all the trails.
If you arive at opening, go with the heard and do the safari first. No need to RUN as the line moves very fast first thing in the morning. We get there 30 min. before opening. Go to the safari first and grab FastPasses and then walk through the standby line. After your first trip you can explore the trail when you exit. When done with the trail, use your FP and take a second safari. We find each safari is different as the animals do roam around.
I would skip ITTBAB with a 4 year old if they get scared by the dark and/or loud noises. If you to give a try, you might have her sit on your lap to avoid a few "surprises."
Don't miss Festival of the Lion King. We usually go later in the day. Getting good seats is hard because of the way the theater is filled. We usually show up right before show time and take whatever is left.
AK is a HOT park so be prepared. Not many attractions/shows have AC. Make sure toake breaks inside shops and restaurants that have AC.
Have a great time and feel free to PM me with questions.