VicR,
I currently own what you are looking for. A 16' Wilderness single-axle travel trailer. It's about 20 years old, but everything works.
I had the axles reversed to UNDER the leave springs to improve ground clearance. The axle flip totally took care of any clearance issues. They are cheap to do as well. My dad flipped the axles on his 25. 5 foot fifth wheel with two axles, so just because a trailer has dual axles doesn't mean you will get any more ground clearance! But flipping is relatively cheap if you are willing to uninstall and re-install the axles. Just take them somewhere where they will weld on new mounting pads. Waaay less than $100.
I also have very limited problem backing the trailer. It is short and light. Even if I start to loose it, I don't have to pull forward very far to retry. I really can't complain. And a short trailer like a 16' with dual axles will be putting lateral forces on the tires and wheels much quicker if you do jackknife it.
The only concerns I have is a tire blowout as mentioned above. So I just try to keep good tires under it. And since it only weighs in around 2000-2500 lbs or so, I'm not maxing out the tires carrying capacity normally. I have to replace tires after time, not mileage because they hardly seem to show wear with such little weight. I'm sure it would pull nicer with dual axles. If I hit just the right spaced dips in the road, it will do a bit of "nodding" or "bobbing", but again, it is so light and short, the leverage on the truck is minimal and not cause for a concern IMO. Longer, heavier trailers benefit more from dual axles than a short 16'.
Oh, and since I have a 4x4, the axle flip made it so I didn't need a 6-8" drop hitch. I can do it with a 4" just fine.
And just to add a few more cents to this ramble, I'd recommend used. Trailers have such a HUGE markup new it is unbelievable. Something like 40% or more. Buying used saves you a lot of wasted $$$ IMO. Even something 3-5 years old will be thousands less. I got mine for only $1900. Money saved can be used for BOMBs.
Steve