No, in Qt you can't do this.
Don't let QWeb's title fool you, but i see young QtWui project.
of course QtWui needs contribute and it's not ready, but it's take benefits to use qt libraries.
Another project also is availabe too, Wt.
Wt is qt mimic, and it's not uses qt libraries because of license and other technical issue.
but as i work with wt let me give you advice, wt itself maybe can't enough for web development because it's just gui toolkit and ......
also there is CppCMS project.
But if you serious about webdevelopment go and take Django mega webframework, django is writed implemented in python.
keep in mind without basic knowledge about html/css/js the webdevelopment life gonna worst for you.
Bookmarks