Let me first refer you to some other threads in the same vein as what you're asking:
http://forums.jetcareers.com/threads/another-new-person.190336/
http://forums.jetcareers.com/threads/dispatcher-career-outlook.190344/
But I'll also give you a short answer that Dispatch isn't as oversaturated as ATC, for sure. Before I went to Jeppesen there were two classes of CTI grads in front of me that still haven't made it into the system for ATC and aren't 31 yet. That being said it's no better or worse than any other sector of Aviation. You'll have to start at the bottom and do your time and it won't be easy at first. I was hired on at a small passenger and cargo operation before I had even taken my O&P but obviously if I hadn't passed it I wouldn't have been allowed to show up to the first day of training. I think you should troll around some of the other threads of Dispatchers starting out and with some lengthy reading you'll actually be able to see their progression from before school, during/after getting their licenses, to landing their first (and sometimes second) jobs Dispatching. It's all pretty insightful, but every case and perspective is different.
