CB
Forget the graduate stuff, although an IT qualification will go a long way to help, what employers are looking for is basic common sense.
In the past the normal career progression was to get a job as a 'Dispatcher', although very many interpretations of that term (see previous posts), with a Handling Agent and then 'prove yourself'. I personally used to interview many people for Ops jobs and if you had a 'Dispatcher' background, then you were almost half way there. It was yours to lose in other words.
I'm fairly sure that it is still the case that you have to start at the bottom and work up and maybe the progression has changed? I'm sure there are others on this forum that can give a more up to date assessment of how things are now?
One thing that I would also like to add is that when I did the job, the money was crap (even worse now, I understand?), however I've never had so much fun in my life! I used to bounce out of bed really looking forward to going to work, there's not many jobs you can say that about now!
Good Luck.