You can achieve this by some sort of custom development
Here is the login
check if it is home page by qa_request() and check if user is logged in by qa_is_logged_in()
than alter $this->main(); in body_content() function
so it would be something like
if((qa_request() == '') && (qa_is_logged_in())){
// your custom code
} else {
$this->main();
}
Now if your condition true for loggedin and home page than you can run custom query for question list by the user.
ould