MediaLab does not have a function to end itself automatically, but you could at least launch Internet Explorer (or any browser) via the Executable item type as the last event in your experiment. Launching it this way will give it full control while MediaLab sits in the background.
You can specify it as the file name of the Executable item with the survey (or other web/local page) included like this:
C:\Program Files\Internet Explorer\iexplore.exe www.empirisoft.com
Or start it in full screen kiosk mode (nothing but the web page) by adding -k between the exe file name and the web address:
C:\Program Files\Internet Explorer\iexplore.exe -k www.empirisoft.com
I believe that if you launch it normally (i.e., without the -k) then it will use whatever settings were applied the last time IE was open (e.g., visible toolbars, whether the window was maximized, etc.). Be careful with that if other people may be using IE between sessions.
Hope that helps,
Blair