Wow.... that is a really young age to begin to manipulate people around you in that way!!
I suppose giving it no attention other than the necessary clean-up would be how I approach it. I agree that taking her out of naptime is too much like giving her what she wants. When she makes herself sick like that and still does not get to come out and play, hopefully she learns that it is not worth it.
What is surprising to me is how she learned that it is even possible to do that!!