Doing "simulation" of a browser will probably not work that well if your application relies on Javascript a lot : there are some crawlers that you can use to test your application, but they don't like JS that much.
The best solution in your case might be to use a real browser to do your testing.
The Selenium tool-suite is quite nice for that : it allows your testing programm to pilot a browser (a real one : firefox, internet explorer, ...) ; which mean having you JS code executed exactly the same way that it would be with a "real" user.
For instance, you can have your testing programm tell a browser to open a page, click on a link, check some content in the page, ... And if there was some JS event plugged onto the link, it will have been executed : there will have been a real "click" on the link.
Using a tool like selenium has some drawbacks, though ; some of them are :
- you need a machine with a graphic environnement, to launch the browsers (command line is not enough)
- tests with selenium take time : browsing and using the application means loading all the CSS/JS/Images/ads/whatever, for each page ; like in a real browser -- because you are using a real browser
But these tests are quite nice, and usefull to test the application as a whole -- ie, more "functionnal tests" than "unit-test".