IPhone 4s iCloud backup restore?

I needed to get a replacement iPhone 4s today. I had backed up my previous iPhone 4s with iCloud the morning it stopped working, while I had the most recent iOS update (6.1). I turned on the new iPhone, ready to set it up with iCloud backup. The backup I wanted was in grey as the new iPhone only had the iOS 6.0.1. How can I get the iPhone to have the back up I want?

Can you not do a complete system restore using the backup?

Don't know what to tell you