Because process of this part is so nervous, my answer might not be the best. Originally, it is better to override core function of application layer. However, it is difficult. I will show easy solutione of theme layer.
Try to add below codes to your qa-theme.php
public function a_form($a_form) {
if(!qa_is_logged_in() && count(@$this->content['a_list']['as']))
$a_form['collapse']=false;
qa_html_theme_base::a_form($a_form);
}
Adverse effect of this hack:
When unregistered user clicked answer button, it will be no reaction in the first time. But, it would be a small things.