I don't have a lot of direct experience milling carbon fiber, but I do know it's extremely hard on tooling. You need carbide, and it needs to be extremely sharp carbide- that is, honed solid cutters, not insertable/indexible.
The CF is incredibly abrasive on tools- and on machine ways, by the way, take precautions there, too- so the carbide is the only thing that will hold up for a reasonable amount of time.
They make special bits for milling CF and PC boards, generally high rake and honed very sharp. If your regular suppliers don't have any on hand, try a big woodworkers supplier- they'll generally have nearly-identical carbide cutters for wood routers that should hold up for a short run.
If milling, use flood coolant. If for some reason you're forced to run it dry, set up a powerful vacuum system with HEPA-grade filters. The dust is nasty and toxic.