As others have pointed out, heat dissipation would make your eyes and brain to explode almost instantly.
Moreover, your vitreous bodies would turn into plasma right away. The interesting thing is that from that moment, it would reflect most of the beam, throwing more energy back to your brain that what comes out of your 'eye'.
The current works related to handheld laser guns take it into account as hitting flesh with a laser would raise its outer layers to plasma, which would subsequently protect the inner layers from the still hitting beam. The solution they propose is to altern periodically between the regular power of the beam and a significantly more energetic beam in order to blow that plasma layer out of the way.
Interestingly, these same works balance the pro of throwing cheaper energy than balistic weapons with the con of the fragility of the lenses. Indeed, the lenses themselves would be progressively damaged by the beam, lessening their optical purity. A decrease of purity would decrease the amount of energy that's sent toward the target. The difference would be absorbed by the lense itself, damaging them even quicker.
The nature of laser itself - light - brings the advantage of range and its proverbial speed, but any alteration of the optical purity of the medium through which it travals would reduce drastically the beam's energy losses per meter. Dust, rain, humidity, you name it.
And even if you can somehow overcome these cons or make it work in spite of them, you'll be the proud living casing of a weapon that can be deflected by wearing light reflecting clothing.
Although they are among the optimum cool, laser beams become pretty quickly dull once you begin to treat them realistically. In your example, I don't see how you can present your character with laser eyes without having that character have some man-made organs, likely its eyes, its whole face and maybe its brains.
Or if it's a magical power rather than a mutation or a technological enhancement, if you're willing to take that road.