Mirroring to another web host for backup and fast re-up

I have a web hosting account on NameCheap which has been down all day because they had a massive hardware fail. Unfortunately they don’t do nightly backups and my nightly backs were going into a directory on the same server. They’re reverting to a two day old backup so I’ve lost two days of blog posts, comments, email etc.

This has got me to thinking about how to better handle this. There is drop box and such remote backups but what I would really like to see is a plugin that mirrors the existing account with all of it’s files, database, etc over to another account which would be on another physical machine ideally in another building and maybe even at a separate web hosting company. Then if the first one goes down in flames I can switch my DNS to the second one which would be within an hour or quarter day or something of up to date.

Does anyone know of a way to do this?