I've got a MacBook Air (original edition) whose internal hard drive seems like it's beginning to fail. Rather than just replacing it under warranty, I'd rather upgrade to a solid state drive. Does anyone have any idea whether this is actually doable?
Yes this is doable. Some things to keep in mind:
You said you wanted to replace while its under warranty? This will void your warranty if you replace it yourself and not by Apple. It is not an easy process to do yourself. My advice is to take advantage of your warranty. There is a very high chance you will leave a warranty voiding trail upgrading the drive yourself.