Corrected your html code so that you have a placeholder for the number of votes.
Corrected the Ajax call so that it passes the same parameters as per the hrefs in your initial upvote anchor.
Fixed various syntax errors in the ajax call
Html Code
<p>
<span class="votenumbers">{$vote}</span>
<a id="upvote_{$qid}" class="q_upvote" href="#"><i class="icon-thumbs-up"></i></a>
<a href="vote.php?q_vote=vote_down&question_id={$qid}"><i class="icon-thumbs-down</i</a>
</p>
jQuery Code
$(".q_upvote").click(function()
{
var vote = "vote_up",
question_id = this.id.split('_')[1],
votedata = "q_vote="+vote+"&question_id="+question_id;
$.ajax({
type: 'POST',
url: 'vote.php',
data: votedata,
success: function(vote_msg){
if(vote_msg== 'ok')
{
//show the new vote
$(this).find('.votenumbers').closest().html(parseInt($(this).find('.votenumbers').closest().html())+1)
}
else{
//show notification
}
}
});
}
)