Hi NellAmerica, greetings from central Kentucky and welcome to the forum.
The GVWR on the 19' International is 4500 lbs., 5000 for the CSA model. The unloaded base weight (UBW) is 3563 lbs. (both models)
https://www.airstream.com/wp-content...tional2011.pdf
According to Edmunds, that model of 4Runner has a 5000 lb. towing capacity when adequately equipped. I can only assume that means with the towing package. The package would include a HD transmission cooler, Group 27 battery, larger alternator, wiring connector, brake controller wiring and frame hitch.
https://www.edmunds.com/toyota/4runn...eatures-specs/
I have the V8 with towing package, 7000 lb. towing, 700 lb. tongue capacity and maximum of 5710 lb. trailer weight. My AS GVWR is 6000 lbs. with a 600 lb. hitch weight and UBW of 4500. I'm well within my safety factor and it handles well, but I wouldn't attempt a larger trailer.
Without the towing package and with the International being at least 3563 lbs. dry weight, I would say your 4Runner is borderline. I wouldn't put too much weight in the trailer, keep the fresh and holding tanks empty when traveling. Definitely get a good weight distributing, anti-sway hitch (I have the Equalizer) and drive in the right lane and keep the speed down, maybe 60 max.
You're going to have to get a brake controller, I don't know if you would have the connection at the driver side kick panel. If you don't have the 7-ping connector or frame hitch, you're going to have to have those as well.
Suggestion: always get the towing package when you buy a vehicle, especially a pickup. It increases the value and makes it easier to sell.
Good luck with your decision.