take a look at qa-include/qa-page-login.php and see if you could pass your way.
Update: $qa_content is the content of a Q2A page. This variable is an array can consist of some key and value pieces. for example $qa_content['form'], $qa_content['custom'], .... Check qa-include/qa-theme-base.php function main_part for that.
When you use $qa_content['form'] in your page, the function form() in qa-theme-base has called. When you use $qa_content['custom'], the function custom() has called and so on.
Then you have two approaches for your work:
1) use some defined pieces for $qa_content on login page
2) define new piece (override qa-theme-base.php functions in your theme qa_theme.php file) and then add appropriate code into main_part function.
Note: Second is better normally.
I hope that could help you continue the way.