do a database backup before anything else.
I’d also suggest backing up teh 3.4.9 folder incase you have made any code changes
yes you can upgrade from 3.4.9 to 3.7.12 – I’d also suggest upgrading to WP 3.5.1
You will have to copy your header images back in, but there is a new option to put them in the wp-content folder – read the on screen documention
if you have made any changes to the actual theme code, you will have to re do them
also be aware that if you have any code in the ‘Content ABOVE the LOOP’, ‘The LOOP’ or ‘Content BELOW the LOOP’ you will have to move it to the ‘index.php’ due to WordPress theme restrictions.
