You might use some of the techniques people use when leaving their kids at daycare. Take a picture of him (or her with him) and let her bring that. Maybe put it in a small plastic frame so it doesn't get all bent up or torn. Let her carry it on her person or pack it in her suitcase. Let her choose a souvenir to bring back home to him.
I would maybe even suggest you let her shop for a new "travel only" bear (or other animal) that only goes on trips with her, lol. We always just let our kids take their lovies. When they were really small, I was the one who was vigilant to keep up with them (they were packed in the suitcases, so no falling out of car doors, and they only came out at night). But as they got a little older I made it more their responsibility. When my son was about 8, he let his snowman in a hotel in Tennessee (he didn't put him in his suitcase like I told him to do, and he dropped on the floor as we left the room). I called the hotel later that day/night, when we discovered the loss. The housekeeping manager had him--the housekeeper had turned him in and the manager was wonderful. She mailed him back to us at our home address, complete with a letter from "Mr. Snowman" telling about all his adventures while he was away from us and how much he missed my son (she had even asked my son's name so the letter was personal).
My daughter, when she was 7, left her stuffed dog "Bob" behind (he fell behind a bed) in a resort condo. We realized it halfway home. Hubby pulled off the interstate at a rest stop and rifled through the suitcases/bags. No Bob. So i used my trusty cell phone to call the resort and they also located and shipped "Bob" back to us.
Maybe we were lucky, but I think mostly we were PROMPT. I suggest to you that most of the housekeepers have kids and know how important these lovies are to our kids and turn them in, hoping the family will call about them.
What I would do (and DID) is explain to your daughter the dangers (getting lost or something happening to Mr. Fluffers) of taking him with her letting her choose whether or not to take the risk. Explain very carefully that it is HER responsibility to keep up with him, keep him safe, and that if he is lost, she won't have him anymore. Then explain that she can choose to leave him at home where he is safe if she doesn't want to take that risk. She is old enough to choose. Unless she is a TOTALLY irresponsible child, then let her decision stand. She will have to live with the outcome either way.
Just my 2¢.