You could copy header.php to child theme and move this code outside #header.
<?php if ( get_header_image() ) { /* if header image is set use it as logo. */ ?>
<h1 id="site-title"><a href="<?php echo home_url(); ?>" title="<?php echo esc_attr( get_bloginfo( 'name' ) ); ?>"><img src="<?php header_image(); ?>" height="<?php echo get_custom_header()->height; ?>" width="<?php echo get_custom_header()->width; ?>" alt="<?php echo esc_attr( get_bloginfo( 'name' ) ); ?>" /></a></h1>
<?php } else { ?>
<h1 id="site-title"><a href="<?php echo home_url(); ?>" title="<?php echo esc_attr( get_bloginfo( 'name' ) ); ?>"><?php bloginfo( 'name' ); ?></a></h1>
<?php } ?>You need some css styling after that.
