IOS 7 iPad keyboard is unresponsive
Anytime iOS is seeming sluggish to me, I like to place it in Airplane mode to see if it's a network issue slowing things down.  For a delay that long, I would then power down the device and restart it while still in Airplane mode. 

At that point you will know if your OS or device has issues to its just doing a lot of work. 

From there, I would start at http://support.apple.com/iPad and start the troubleshooting assistant to narrow done the cause.