We towed a 1000lb popup with a Suzuki Samurai for many years without issue. Then we towed a larger 2000lb popup with a 4 door Suzuki Sidekick which did very well. Both were 4cyl. On both vehicles I did add headers and a less restrictive exhaust which helped greatly but they did fine before the change.
Depending on year, the 4cyl Rav4 has a tow capacity of around 1500lb's. That is with only the driver and no luggage. A 1000lb popup trailer would be the limit for the Rav4. A V6 4 door mini truck would do far better (I towed for years with a 1993 Nissan V6 truck).