The answer in the manual is that the Prius is not designed for towing. That said:
1. There are hitches for the Prius but they are for hitch mounted racks so they don't have electrical connections or safety chain loops.
2. Prius owners have towed very light trailers on occasion for short distances with no known damages. Very light means 300 to 500 lbs. total weight. Total weight means the trailer plus contents. A U-Haul trailer is way more than that. I strongly recommend against pulling a UHaul trailer with a Prius.
3. The Prius' braking system isn't designed for towing, so handling will be a problem.
4. The Prius monocoque construction doesn't include reinforcements for trailer hitches.
5. With two extra tires on the road plus a bunch more weight, MPG will go down dramatically.
If you still want to try it, you'll have to fabricate the electrical connections and safety chain eyes. Then you'll need to get a Scangauge (
http://www.scangauge.com/ ) and watch the water and inverter temperatures very closely. I think it will be cheaper to ship the furniture--make that way cheaper. It will also be a lot safer. I would not do this if it were me.