Does the FAA advise or require pilots to wear eyewear designed to protect them from lasers?
I'm not aware of FAA (or any other regulatory body) recommending protective eyewear for lasers. FAA safety Advisory doesn't include them. There are a couple of problems with using protective eyewear for lasers:


The eyewear is usually wavelength sensitive; The pilot has to wear the correct eyewear that blocks the incoming laser beam; he/she should know the wavelength of incoming laser.
The protective eyewear filters (atleast most) of the incoming light in that wavelength. This may affect the normal sight of the flight crew.


Due to these reasons, the regulatory authorities are more concerned with procedural changes that protective wear. From Boeing's protection against lasers:


  ... however, airlines should consider the drawbacks that are associated with them. Filtering light reduces the total amount of light entering the eye, which can adversely affect normal viewing, ... . In addition, filtering green light can remove some green flight symbology on flight deck displays and change the appearance of some of the other colors used. As a result, protective glasses should be used with care.