Looks like the '06 is rated to tow 5000-7300 lbs, depending on how it's configured. You'd need to know which yours is.
Issues you'll likely encounter:
1. After loading, that trailer will be right at, or over, the upper range of the 4runner.
2. The 4runner has a short wheelbase, and relatively high center of gravity. You'd need a really good hitch to tow a trailer of that length (Hensley, ProPride).
3. Take a look at the sticker on the driver's door pillar of the 4runner to see what the capacities are for the vehicle payload. A trailer of that size and weight will have a tongue weight of something like 750-900 lbs. How much total payload does that leave you? What else are you planning to put into or on the 4runner (people, pets, stuff), and how much does it weigh?
4. Take a look at the sticker on the 4runner's receiver - can it handle that TW?
5. Consider that you're looking at doing this with a 10 year old vehicle, and consider how well that vehicle has been maintained and the condition it's in. (Could be great, could be iffy. Include things like: When repaired (if it needed any) were Toyota parts used, or aftermarket parts? Were they critical items?)
In modern cars, the engine is rarely the limiting factor.
2021 Four Winds 26B on Chevy 4500