'post_date' => '0000-00-00 00:00:00',
'post_date_gmt' => '0000-00-00 00:00:00',
'post_modified' => '0000-00-00 00:00:00',
'post_modified_gmt' => '0000-00-00 00:00:00'
эти сроки отвечают за добавление даты.
Делай так:
$new_post_date = current_time('mysql');
$new_post_date_gmt = get_gmt_from_date($new_post_date);
$args = array(
'comment_status' => $post->comment_status,
'ping_status' => $post->ping_status,
'post_author' => $new_post_author,
'post_content' => $post->post_content,
'post_excerpt' => $post->post_excerpt,
'post_name' => $post->post_name,
'post_parent' => $post->post_parent,
'post_password' => $post->post_password,
'post_status' => 'publish', // черновик, если хотите сразу публиковать - замените на publish
'post_title' => $post->post_title,
'post_type' => $post->post_type,
'to_ping' => $post->to_ping,
'menu_order' => $post->menu_order,
'post_date' => $new_post_date,
'post_date_gmt' => $new_post_date_gmt,
'post_modified' => $new_post_date,
'post_modified_gmt' => $new_post_date_gmt,
);
