I think you'll need a handler in your plugin to manage the request.
E.g.
add_action('wp_ajax_myplugin_getdata', 'myplugin_getdata');
or
add_action('wp_ajax_myplugin_getdata', array($plugin,'getdata'));
if your plugin is in a class with $plugin as your plugin instance.
In ajax.js you need to execute a GET with an action parameter matching the action above minus the wp_ajax_ bit,
e.g.
$.ajax({
type:"GET",
url: http://myblog/wp-admin/admin-ajax.php,
data:"action=myplugin_getdata&"+data,
success: function(returned_data) {
$('#display').html(returned_data);
}
....
then in myplugin_getdata retrieve your GET parameters, perform a database lookup and issue a
die('My returned data');
You can get the AJAX url via admin_url( 'admin-ajax.php' ) and pass it to the ajax.js after calling wp_enqueue_script via wp_localize_script.
For non-logged in users you'll also need a,
add_action('wp_ajax_nopriv_myplugin_getdata', 'myplugin_getdata');
Ian.