A 6000 lb car on a suitable trailer will total around 8000 lbs or so -- does your RV presently have a 10K hitch and rating? Also be aware that a 16 foot 7500 GVWR rated trailer often only has a 4,200 to 5,500 payload rating so a 6000 lb car will be an overload.
Further, you have to consider where you will store/park the open tandem trailer when you are at your destination, as many RV parks have very limited storage parking.