OK, take a deep breath. lol I would wait, at least a couple of weeks, before ordering a replacement. A few years ago we were at MGM w/our then 8-yr old niece. She had bought a yellow cap with Princess written on the front and WDW written across the back. Really cute. We found it at the outlet store for $5 (what a deal!). She left it on the Backlot Tour vehicle and we didn't realize it until several minutes after we exited the ride. She was devastated! Well we filled out a report with lost and found. I called the next couple of days but no dice. We didn't make it back to the outlet store so she didn't get a replacement. Oh well. At least we were only out $5.
Lo and behold, several days after we returned, I get a package in the mail from Disney. It was the hat! THE hat. I mean, there must have been a million of them made, it didn't have ANY personal markings on it. They also just mailed it and didn't make me pay for it. I was impressed!
So like I said, take a deep breath, and wait. Maybe I was just really lucky, but I would think that if you left it in your room, it had her name embroidered on it, chances are, they'll mail it to you.
Best of luck!