Carbon fiber won't rust. It's made of strands of carbon fiber which are then woven into a "fabric" which is flexible until it is cured. Once cured, it becomes quite rigid despite its light weight, which is why it's also a good material for making airplane surfaces. It will chip if struck hard enough, and it might burn, but it won't rust.
In terms of durability G10 fiberglass seems to be the toughest of the popular handle materials, followed by canvas or linen micarta, then closely followed by carbon fiber, at least based on what I've read here in BF.
I'm sure if I'm wrong, someone else will correct me.