Amazon is reputatble, but the marketplace sellers on there may not necessarily be. It's worth asking if she bought it from Amazon directly or from someone on Amazon, and if the latter, what their feedback as a seller is like.
That said, I don't think you have anything to worry about quite yet - it's the Christmas period, so the postal service is going to be working overtime. Amazon have their own courier service now, but they'll be stretched to the limit as well I think. You can keep track of the order online - don't panic unless it misses the estimated delivery date.