This doesn’t have much to do with Genesis, other than you need to hook into the header in one of several ways, with Simple Hooks http://wordpress.org/plugins/genesis-simple-hooks/ or in functions.php. I’ll leave that to you.
But using
<?php echo qtrans_getLanguage(); ?>
do something like this:
$currentLang = qtrans_getLanguage();
if($currentLang == 'fr')
{ //show french logo
$imageName = logoFR.png';
} else
if($currentLang == 'hi')
{ //show Hindi logo
$imageName = logoHI.png';
} else { //show english logo to rest
$imageName = logoEN.png';
}
Or, name your images appropriately:
<img src="http://mysite.com/logo-<?php echo qtrans_getLanguage(); ?>.png" />