I just came from posting in a bowling thread, perhaps she wouldn't mind going bowling at Red Rock Lanes at the Red Rock casino hotel.
That's a little over 10 miles from the strip though.
South Point has a 64 lane bowling alley and it's only about five miles south of the airport.
I would think since your daughter is hyper, bowling is a good way to wear her out a bit.
Vegasnut also made a few good suggestions to calm down a restless youngster, or hype her up a bit more.