You might want to have at least RAID 1 solution. The way RAID 1 works is that it will write any bit of your data to two different HDs (called mirroring). That way when the first HD crashes, you should not worry much (Except down time) since you have all of your data on the other drive.
But the thing, is the dedicated server RAID capable? If not, then yes ... you can just add a second HD and use cron job (every hour, every day, whatever you choose) to tar/zip or even just mere copy of your valuable data on the main HD to the second HD. In the event when your main HD crashes, all you need to do is to replace your main HD, reinstall the OS, and copy your valuable data from your other HD back to this main HD ...
Off-site backup is another solutions ... On-site backup to the NOC's tape backup is yet another solution ....
But anyway, I don't think the downtime would be in minutes region, unless it it is RAID
cheers,
