We've visited in the spring (though not with our DD); it was a distinct and very lovely time of the year-- not yet too hot for hiking even long distances, UNCROWDED...
and baby animals everywhere. The snow melt also meant that the falls were spectacular-- beyond description, really. But in addition, parts of the upper loop were closed because they hadn't yet been cleared.
Still, if I were taking DD I think I would try for spring or fall. It was an amazing place. Grand Teton is also amazing, but probably not quite as flamboyantly appealing at this age.