Oh, 600lb is *much* lighter than I was anticipating. Make sure to verify that because most teardrop camping trailers I've seen are 1000-1500lb.
Look at the trim plate inside the driver's door sill. It will show GVWR -- Gross Vehicle Weight Recommendation. The car itself is 2405lb for the manual and 2485 for the automatic, then add the weight of persons and cargo, and your 600lb trailer. If you're under the GVWR you should be ok. Here are some things that will make you more successful:
- If it's an automatic, I recommend that you install a transmission cooler. Find a generic one, and a good independent servicer, and they'll smile a bit but they will install it for you. :) This will keep your transmission healthy when you load the vehicle down, especially in hilly terrain.
- If it's a manual, you might need a new clutch or even just a heavier clutch. Because the Rio isn't really used by the performance enthusiast market or towing (hehe!), you might not be able to find a stronger clutch. But it's worth researching.
- Make sure your brakes are up to snuff: good pads and rotors, proper bleeding, high performance fluid. Not racing brake fluid, but for example Valvoline SynPower DOT4+ fluid boils at over 100 degrees higher than cheap Prestone DOT3-- and it's like $3 more per 12oz. Your brake pads, rotors and brake fluid will get hotter when towing.