this is indeed hardcoded in the page template. You can either upload an image with that same name and place it in the theme folder/images/ subfolder, or you can modify the template code and add code for the image of your choice.
To do so, go to wp-dashboard > Appearance > Editor and open home_option.php. Locate the following code and change to your likings:
[img]<?php bloginfo('template_url'); ?>/images/headshot.jpg[/img]" />
hope that helps, if your site is online, we could perhaps provide more targeted support and directions,