Ok, unfortunately I cannot see your file, but here is what I should do: in the header.php search for the div id=’nav’ element and add the following lines just before the /div closing tag like this:
<div id='nav'>
...
...
...
Add these lines:
<div style='float: right;width: 320px;'>
<?php echo do_shortcode('[wpdreams_ajaxsearchpro id=1]'); ?>
</div>
and stop.
</div>
This will create a container element for the search and it should appear where it supposed to.