Nice choice, i'm not long back from backpacking solo around central and south america, and it's bloody fantastic around there!!!
Definately not true. Central and South America are very well set up for backpacking. South America has some of the best coaches i have ever been on. Both Central and South America have extremely good long and short distance bus systems that are good quality, take you anywhere, and are very very affordable. If you're feeling adventurous in central america you can get the local chicken buses around, they cost near nothing and are an awsome experience!!!
2. would be unsafe for a girl to travel alone
Again, definately not true. This is a very common myth about Central and South America. I met heaps of girls that were travelling solo around central and south america and they had no problems. It's no more dangerous than Europe.
My trip through Central and South America was part of my first ever backpacking trip and i did it solo, so don't let lack of experience scare you off, if i can do it anyone can!! I went to Mexico, Belize, Guatamala, El Salvador, Peru, Bolivia, Chile, Brazil, and Argentina. I had absolutely no problems, nothing got stolen, i never got mugged or harrassed.
Central and South America have A LOT to offer and you shouldn't miss out!! I enjoyed these places way more than Western Europe and i'm definately going back in the not too distant future.