Interactive Calendar plugin?

Hi,

I am interested in finding a way to integrate a calendar into a doctor’s website. I want patients to be able to access the calendar and sign up for appointment based on available time-slots. After a patient has selected a slot, the slot becomes closed and the patient receives an e=mail notification of their appointment. Is there a plug-in for wordpress that would accomplish this? If not, how would I go about developing this kind of application?