update database with jquery and php

i try to update/edit using jquery and then save it to database with the help of php

the problem is i cant pass the new data to php or php didnt receive data from jquery

here is my form

<form method="POST" name="postForm" action="update.php">
<div id="edit">
First name:<input type="text" id="firstname" value="<?php echo $row['firstname']; ?>">
</div>
</form>
<button id="button">Edit</button>

and this is my script of jquery

jQuery("#edit").dialog({
    modal: true,
    resizable: false,
    draggable: false,
    autoOpen: false,
    width: 400,
    buttons: [
        {
            text: "Ok",
            click: function() {
                jQuery.ajax({
                    type: "POST",
                    dataType: "json",
                    url: "update.php",
                    async:true,
                    data: { dataToUpdate: jQuery('#edit').attr('value') }
                });
            }
        },
        {
            text: "Cancel",
            click: function() {
                jQuery(this).dialog( "close" );
            }
        }
    ]
});

// Link to open the dialog
jQuery("#button").click(function(event) {
    jQuery("#edit").dialog("open");
    event.preventDefault();
});

and this is my PHP

  $id = $_GET['id']; // i dont know if i should put it or not to identify the info i want to edit
  $firstname = $_POST['firstname'];

  $sql = "UPDATE info SET
        firstname='$firstname' WHERE id=$id";

        $result = mysql_query($sql);

        echo json_encode($result);