PLQ is shorthand for "peer-like qualities."
The qualities generally required of a person before they are elevated to a Peerage, whether it is the Chivalry, Laurel, Pelican, or Order of Defense, in addition to the martial, artistic or service skills specific to the award. It's an easy acronym for a complex set of concepts.
Some online essays on the subject: (please note that different writers in different kingdoms may have varying viewpoints.)