MySQL dump over SSH to a remote host
Original Article - http://christiank.org/wp/2010/12/pipe-a-gzipped-mysql-dump-over-ssh/
If you want to take a SQL dump from some host, compress it and send it across SSH to another host then this is the command you are chasing
mysqldump -u MYSQL_USERNAME -p YOUR_DATABASE | gzip -c | ssh USERNAME@YOUR_TO_HOST 'cat > ~/dump.sql.gz'