This the standard vB code for the quick search:
HTML Code:
<form action="search.php" method="post">
<input type="hidden" name="do" value="process" />
<input type="hidden" name="showposts" value="0" />
<input type="hidden" name="quicksearch" value="1" />
<input type="hidden" name="s" value="$session[sessionhash]" />
<input type="text" class="bginput" name="query" size="20" /> $gobutton<br />
</form>
Just change it with the added forumid.
PS In your example you seem to be missing the 'do', also don't use full url's, better relative file ie "forum/search.php........"