Create a header for your child wordpress theme

If you want to personalize your header in your child theme, you can do it without modifying the header.php from twentyeleven.  You can copy the header.php file onto your theme’s folder and then start modifying from there.

Copy header.php from twentyeleven theme on wp-content/themes/twentyeleven and put it in your theme’s folder.

After that, you can safely modify the header.php from your theme’s folder without loosing your changes when there’s an update to twentyeleven theme.