Lola, First let me say kudos to you for planning such an exciting trip! Sounds like an amazing time.
Next let me note that I am a Vespa fan, and I do have an older P200E like has been mentioned. I am not here however to recommend that, nor would I recommend any Vespa for an extended trip through South America. A trip across the US, certainly, but not outside of US borders.
If it was me and I was trying to keep the size down but the usability and reliability factor high I would look seriously at a small dual sport, especially one with a carburator for simplicity. Please do some research on the Kawasaki KLX250s. They have been making them for quite a few years, and released a new version in 2009. Lots of accessories are available to hang racks, bags, engine guards, hand guards,etc. I realize it's not cute like our scooters, but the larger wheels and off road tires will give you the ability to get through most anything you will encounter. Also, I would expect reliability and more importantly durability to be significantly higher over rougher roads.
Best of luck to you regardless of what option you choose. I just hope you'll at least consider other options before settling on a Vespa.