use
Net::OpenSSH!
my $ssh = Net::OpenSSH->new('rsync.hidrive.strato.com',
user => 'account-xxxx',
key_path => '/root/.ssh/rsyncstrato');
$ssh->error and die "unable to connect to remote host: " . $ssh->error
+;
$ssh->rsync_put({stderr_file => 'rsync.log'},
"$foMy/$fMy.gz",
"/users/account-xxxx/backeups/mysql/$tLog/")
or die "rsync failed: " $ssh->error;
BTW, it is not a good idea to use rsync for something that is generated on the fly and then compressed. That usually makes the rsync algorithm useless and inefficient. Just send the file uncompressed.
Another way to optimize rsync transfers is to place an old version of the file being transferrer (i.e. the backup from the previous day) at the destination.