The 4Runner is a great vehicle and will tow that with ease. Just about any mid size suv with a V6 should handle it.
If you do go with an older (03-09)4Runner I would suggest considering the 4.7 V8. Not that it's needed to tow a Casita, the V6 is power enough, but the V8 is a much smoother and stronger engine. I've owned and towed with both V6 and V8 models and the difference in price and MPG is almost negligible. Less than 1mpg difference non towing and the V8 actually got better mpg while towing as it didn't have to work as hard.
The V8 has better tow gearing, less hp but more torque, comes with a transmission cooler and is rated to 7200lbs should you wish to go bigger in the future. Most V8s (but not all) came with the frame mounted receiver as opposed to the lesser cross member mounted one. If you plan on using a weight distributing hitch you need the frame mount receiver.