I don't think such a plugin exists. I'm thinking about some kind of plugin that interacts with some kind of online calendar by means of an API, so that you could see and and events. It sounds like a weird addition to a question and answer site.
Implementing such a plugin would take quite a lot of time. A different story would be to embed some kind of existing calendar in a read only mode (Plan B). Still you would have to make a plugin (I'm thinking about a page plugin http://www.question2answer.org/modules.php?module=page) and embed the code of an online calendar that would allow you to do so.
Plan C would even be simpler and it would involve adding a link from the admin/page section to the online public calendar (fair enough, in my opinion).
I would give it a try to some kind of online calendar (I only use Google Calendar but there are plenty more http://mashable.com/2007/10/08/online-calendar-toolbox) that would allow events to be publicly seen. In the case of Google Calendar make sure to set the calendar public (https://support.google.com/calendar/answer/37083) and from the calendar settings you can find the HTML code to embed (Plan B) the plugin and also a section with the calendar addresses (XML, ICAL and HTML). AFAIK, if you set the calendar to public and configure the link in Q2A to be the same to the one advised when pressing the HTML button then you'll be fine (Plan C).