I'm no expert on GTPs as I just got my first one about 7 months ago. BUT, I think your perch is too big around for such a little guy. My adult (5 foot long!) GTP was on a perch that size when I got it and I thought it was too small. I was told by some long-time GTP owners and breeders that they perfer a perch skinnier than you would think. I upgraded my cage to a PVC cage and put multiple size perches in and she has chosen the smallest perch - a little bigger than yours'. My baby is about 3 inches in diameter (empty)!
I've seen GTPs the size of yours on perchs about as big around as a pencil or slightly larger. Can you add more than one perch to give her a choice?
Andy