I started with a 12,000 lb hitch when I bought my camper. It was 8,200 lbs dry with a tongue weight of 1,100 lbs or so. I always felt like the hitch was undersized. I have never weighed my tongue but would guess it to be around 1,200 - 1,300 lbs. I did weigh the camper on a trip home from a camping weekend and it sat around 9,500 lbs. I recently upgraded to a 14,000 lb hitch and will say the difference was well worth it. After the initial adjustment I was able to bring the front of the truck back to the exact height as it was unloaded. My rear only sagged 1 inch. It was dead on the money. I could never do that with the 12,000 lb hitch no matter how much tension I put on the bars. After one tow I lowered the brackets because I felt like the trailer was trying to steer my truck due to the friction on the bars. Now it rides perfect. The heavier bars help to reduce the rear end bounce I was getting with the lighter bars.
It looks like your trailer is close to mine when it comes to weight. I would get the 12,000 lb hitch at the very least but would upgrade to the 14,000 lb hitch if you can swing it. I think you'll appreciate the extra weight capacity.
2001 Ford Excursion 6.8L V10 Limited
2012 Sabre 32QBTS
Dear wife, three sons and one dog