Hold on a sec here, I don't know weather one detail in the requirements list has gone unnoticed by the majority here (I know DIABLO mentioned it), the Samsung NC10 or any of the Atom Netbooks will do everything you asked just fine, except, run WoW properly.
I have an NC10 right here, and it does not run WoW anything close to what I would call 'properly' with all the graphical settings at the lowest. It will run WoW classic, in Azeroth on the lowest settings ok and it's tolerable in the now rather empty Outland for levelling purposes but the Wrath of the Lich King content, no chance, it's a slide show.
If you want to run WoW properly, you are going to need a 'proper' laptop I am afraid, you can get some pretty decent small ones though. Samsung's very own Q210-AS04 would do the trick, its not a powerhouse but it's got a 2GHz C2D and a Geforce 9200GS graphics chip in it and a 12" display, it's pretty small and light although obviously not Netbook small and light, but it will run WoW properly if you keep the quality settings low in the WoTLK content and it will run the old content with much better settings. Really though, if you play WoW seriously enough to be into raiding and such, you will need something much more powerful than you can get in this size bracket, you would be back into the 15.4" category really.