I hate to disappoint you, but a 100% carbon fiber plate won't have the rigidity you're going to want from a hard plate. If you make a lay-up with some other material to add rigidity, you might be okay.
It's also remarkably easy to crack carbon fiber if it flexes. I'm not sure what makes you think otherwise. I've seen CF kayaks completely destroyed from a collision with a rock at 6 mph. I have a CF paddle I built (yes I built it "properly") that also broke. It would work for a while, if you had say, 6-10 layers of 6 oz cloth laid up. I've been thinking of experimenting with a fiberglass or CF/plywood plate just for fun, but I have so many other projects I probably won't get around to it.
For what it's worth, a PVC plate is significantly easier to make than a CF one would be and works quite well. For the weight savings, you're not gaining much over AL when you consider a CF plate will probably cost a lot more and would certainly cost you more (in time alone) if you were to make one.