I think this is a bit paranoid, because gmail is used by a lot of companies worldwide (it's a feature of gmail). If you have a domain, gmail can handle all the mails for it. It's very unlikely that gmail stops its activity in the next decade.
Anyway, it's always a good idea to store data in (at least) 2 different locations. In the case of gmail, the simplest way to "backup" existing mails is to use an IMAP client which will replicate everything that's currently on the server (mails, folders, and a lot of informations), without deleting anything on the server.