I am a web developer and would like to debug a webapp/website on a Windows Phone device. It would be neat to have some kind of window where I can see the javascript console.
I don't think so. But you can use IE10 and change the User Agent string to simulate you are IE10 in Windows Phone.
Edit
I think all JavaScript functions in the mobile are supported in Desktop. But if it is not a solution I'm afraid your only friend is this :
Compact Inspector