I have noticed significant slowdowns in the expansion areas myself, since they are much more graphically intensive than older areas.
I don't know what to do about it yet, but since WoW's system requirements have gone up with the recent expansion, you may want to check if you need to upgrade anything.

If you post the basic specs of your computer I can probably let you know off the top of my head if it is reasonable to think that may be the probable cause of the problem.