I've never brought my hamster to T, but actually brought part of my horses: I've braided a strand of each my horse's tail and cut it of. I've got both braids with when in T and as it's comforting to know they are in my bag. I once had to take them out and hold them during a difficult session and my T was great about it even when I felt silly.
Might be because she's got horses too... and actually invited me home to see her foal in the spring. Not sure I'm going to accept that offer though...