Copy the file YOUR_SITE/modules/search/search-result.tpl.php
to your theme and modify the code inside with this:
<?php
//obtaining the username
$username = explode('(', $title);
$username = trim($username[0]);
//getting the user object
$user = user_load_by_name($username);
?>
<li class="<?php print $classes; ?>"<?php print $attributes; ?>>
<?php print render($title_prefix); ?>
<?php
/*
* The following line will print the user picture
*/
print theme('user_picture', array('account' =>$user));
?>
<h3 class="title"<?php print $title_attributes; ?>>
<a href="<?php print $url; ?>"><?php print $title; ?></a>
</h3>
<?php print render($title_suffix); ?>
<div class="search-snippet-info">
<?php if ($snippet): ?>
<p class="search-snippet"<?php print $content_attributes; ?>><?php print $snippet; ?></p>
<?php endif; ?>
<?php if ($info): ?>
<p class="search-info"><?php print $info; ?></p>
<?php endif; ?>
</div>
</li>
This will be the output:
EDIT: If you want follow another way you can read this: How to access to the user info on the search page?