Yes, it's fairly easy to lay things up in carbon fiber. I posted about several items I made, including this knife sheath:
The investment to get started doing hand layup of carbon fiber is about $30 in epoxy, $35 in carbon cloth, and $30 in other incidental stuff (a roller, tape, masking plastic, foam, clamps, etc). That amount of material would provide for lots of projects.
Dan Y., I would recommend using a minimum of two (three is better) layers of reinforcement for two reasons. First, it ensures that no epoxy-only voids in the weave of the reinforcement will penetrate through the entire thickness of the part. If you hold a part made with a single layer of heavy cloth up to the light, you'll see spots of light arranged in a grid where there are gaps in the weave of the cloth. Carbon fiber reinforcement cloth tends to be very loosely woven to avoid air entrapment (to permit the epoxy to fill all the spaces). If you use more than one layer of lighter cloth, any epoxy-filled voids in the weave will be shallow (and reinforced by carbon under or over it). Second, using more than one layer of lighter cloth allows you some flexibility in the way you design the reinforcement. You can align the layers so all the reinforcement goes in two directions, or you can rotate them so you have reinforcement in 4, 6, 8, or more directions.