redirect parent pages to child

I’d like to apply the following code to categories:

<?php
/*
Template Name: Go to first child
*/
	$pagekids = get_pages("child_of=".$post->ID."&sort_column=menu_order");
	if ($pagekids) {
		$firstchild = $pagekids[0];
		wp_redirect(get_permalink($firstchild->ID));
	} else {
		// Do whatever templating you want as a fall-back.
	}
?>

If it worked for categories, then I’d be able to show the firse child category content when its parent is called for example via permalink.

For example:
https://www.mydomain.com/parent/ would go to https://www.mydomain.com/parent/child

I need this because my parent categories are empty and if you go to https://www.mydomain.com/parent/ you see no contents, only fotter/sidebar/header

thanks!