Your Rails (3) version should be fine but, unless I've misread the related Heroku docs, Cedar requires Ruby 2.0.0 (it could be that their getting started docs are requiring Ruby 2.x just for the tutorials).
Given the base box/OS used on Cedar (Ubuntu 10.04), it's hard to imagine 1.9.3 would not run. That said, and for what it's worth, I've upgrade three different Rails 3.x apps from 1.9.3 to 2.0.0 and then 2.1.1 with zero problems.