There is one simple way to find out that Mists of Pandaria does not require a hardware upgrade. If in the past you have clicked on the “Recommended” button from System/Graphics, you should have those settings even now.
Take a screenshot using the “print screen” button from your keyboard with the current settings and go to any zone in Pandaria, click on the “Recommended” button again. You should see no changes.
If you experience any “spikes”, check if anything is running in background, also lower the settings for “shadow”, these seems to require a lot of hardware resources.