An Artist I follow recently posted a Tutorial on making a floppy beanie plush. I imagine it would be possible to modify the patterns to make a quadruped dragon floppy beanie. Beanie Tutorial
I'm at a mid-way point making a few plushies of my own, (Milotic and Aurorus from pokemon specifically), but MAYBE after i'm done with those I might try to make a dragon plushy. I have no idea which dragon I would attempt however.
Those of you who want a plushy but don't want to make/attempt to make it yourself may want to consider commissioning an artist. It'll cost more than getting a machine