Have you considered looking into using felt, and then needle felting roving into place to give it a more fluffy texture? It would be way time consuming, and would essentially ask that you learn a secondary craft... But look up some tutorials - it may give you the look you want? I know I've seen some pretty fluffy things come out of different felting techniques.
I can't say I've seen a fabric that will do that naturally, just from long fibers, and still look good - not like a stuffed animal that has had the fluff loved out of them... The minky may be your best bet - it does have a plush, soft look - maybe not cotton candy, exactly, but it would still have a fluff to it?
Convention Line-Up: BronyCon 2015 - Dragon*Con 2015
1950s Celestia (MLP:FiM), Undead Death Knight Starter Gear (WoW),
Lorna Dane Serval Industries (X-Factor), Adult Loki (Loki: Agent of Asguard)