Is carbon fibre dust dangerous to sand, and what precautions do I need?

It is sensible to take it seriously. Carbon dust from sanding or machining is a fine mechanical irritant to the skin, eyes and lungs, and while it is not in the same category as something like asbestos, it is not something you want to be breathing. It is also electrically conductive, so the dust can find its way into electronics, power tools and switchgear and cause shorts, which catches people out. For protection, wear a properly rated dust mask or respirator, along with eye protection, gloves and covered arms, and keep the dust down at source with extraction or by wet-sanding where you can. Work in a ventilated space away from anything electronic, clean up with a vacuum rather than blowing the dust around, and cover nearby equipment. A bit of preparation keeps the job clean and safe.