Please find below a list of Q adjectives which might be used to describe a person.
quack
quaint
qualified
qualitative
quantitative
quarrelsome
queer
queerer
queerest
querulous
questionable
quick
quicker
quickest
quiescent
quiet
quieter
quietist
quirky
There are many more lists of adjectives on this website. For more adjectives starting in Q, see this post containing a large number of adjectives beginning with the letter Q, some of which can be used for describing people.