Asking for input/help diagnose, not an a-body

My granddaughter has an Infiniti Q40 (06 model, I think). It is 4wd but not full time. When you hit a bump just right at 40 mph or so, it will begin to shake the rear of the vehicle left and right as if it were dancing. It has a conventional rear end under it. Only cv axles are under the front. I can see that it has never had rear shocks or front struts replaced. In all my years I have never experienced this condition.