Where you take the carbine class (who teaches it) has a lot of bearing on what you will need. I have taken several carbine classes at both Gunsite and Frontsight. At Frontsight you would be fine carrying one extra magazine in your back pocket. At Gunsite, you would be at a huge disadvantage and I honestly don't think it would be worth taking the class like that. At Gunsite, I carried as much ammo as I could: at least six 30 round magazines and still ran out.
One item you really need is a LULA:
http://www.bushmaster.com/shopping/magazines/8448670-lula.asp
When most people shoot recreationally, they load a magazine and shoot the gun until it is empty, then reload the gun and keep going. THis is considered very bad form in a defensive situation. One of the big lessons taught in formal classes is that you keep you gun fully loaded when ever possible. If you engage a bad guy and things settle down, you reload your weapon as soon as you think it is safe to do. You might have fired one round, you might have fired 15 rounds, odds are you really have no idea how many rounds you fired: you fired as many as it took. If you need your weapon again, you want it fully loaded. Anyway, when you come off the line, you are going to have a bunch of partially loaded magazines. You need to top them off. Sometimes you want to quickly unload a magazine and put it's contents into another partial magazine. Whatever: in a class you are doing a lot of loading and unloading and this tool speeds things up and saves a lot of wear on your fingers. You will be happy with it.
Looking at your gear, IMO you need three main things. A sling, an optic, and a light. Along with magazine pouches, plenty of magazines, and the LULA.
In all the classes I have taken, I got tired physically (and mentally). You spend a lot of time standing on the firing line with your weapon in your hands. Again, this isn't plinking out on the back 40 where you can just set your gun down. You need to have a tac sling to support the gun to give you arms a break. A carry strap doesn't get it. You need to be able to have the gun in the low ready (cheating low ready to get a little rest) and have some of the weight supported by the sling. I prefer a single point sling, specifically the one by The Wilderness. I have used that single point sling in four carbine classes and two shotgun classes. That is something like a total of 27 days of at least eight hours a day carrying a weapon on a sling: my choice has been tested.
Optic: You will quickly appreciate an optic both day and night. The one to buy is the Aimpoint ML2 or ML3.
Light: all the classes I have taken have included at least one night shoot. You will need some kind of light that you can use while you are running the carbine. I choose a Surefire 900 series weaponslight, you can get by with less, but it needs to be something LIKE a smallish "tactical" flashlight. Big Maglites and stuff like that are not the way to go.
As was mentioned, this has been covered numerous times: do a search and you will find some reading material.