There are only 846/171,476 (.49%) words that begin with the letter Q in the English dictionary. 

Qadi: A judge

Qanat: sloping underground channel or tunnel constructed to lead water from the interior of a hill to a village below

Quirt: a short-handled riding whip with a braided leather lash

Quip: a witty remark

Quash: reject or void, especially by legal procedure

Quinquennially: occurring once every five years or over a period of five years

Qualmishness: overly scrupulous