Yep, you can change your class. You do that in the Guardian hall. (In the space station, that's the 5th floor). There's a desk person to talk to, if you want to switch classes. Raising your class is all about the Mission points you get from completing a mission. Try not to let anybody die for the better mission grades. Better grades help increase the amount of awarded mission points for you. However, a word of warning, Mission points awarded are much less online than they are offline. This is mainly because they designed it so that you increase levels and such faster offline than you would with your online characters.
It doesn't take too long, though. That's one of the reasons to not stick with the easiest, lowest missions for too long. Once you gain like 5 levels, it's best to search for missions more akin to your level, and ones that have better level requirements, for the better mission bonuses. You also will more likely fight monsters that give you better exp, for your general character level. (You'll start to see missions that have a level 5 req, or a level 10 req, or a level 15 req, and so on.)
It's one of the reasons I was urging Magician to go to Parum and do some missions down there. It's the general next logical progression to keep your gains coming faster, as I experimented with, in the offline sessions.