Good advice from Roger. From my experience with our 16' Scamp (no lift), the trailer will handle anything reasonably navigable by a minivan. I'd be more concerned about the damaging the exposed plumbing than any potential suspension problems.
We've camped a fair amount at Croatan, Uwharrie, Pisgah and Nantahala NFs here in NC and have found some really great spots 'off the beaten path'. There are also trails in each that I wouldn't attempt with my lifted and locked Wrangler.
The Scamp even survived a trip to Portsmouth Island although we had to leave the wife's new Tacoma five miles up the beach when the rear end blew. Toyota covered the $900+ recovery charges and all repair work but I'm still getting razzed by our daughter for having to rescue us and the camper with her old Blazer.
So far, the most damage we've suffered was when the microwave
broke loose on a particularly bad stretch of I-95 in SC. The inside looked a lot like what Andy and Susan described.
Use a little common sense and you should be fine.