I am very happy that you are interested in TeamPulse and the REST API.
Unfortunately, we don't support windows authentication via ajax request. You could achieve this via .net sdk. As workaround I could propose to you to display teampulse login page to the users and after that redirect them to you page, something like http://server:9898/Authentication/Restrict?ReturnUrl=[your_url].
If windows authentication is very important for you we could try supply a sample, but we will need some time.
I hope this will be helpful for you.