Yes, there is a four (4) letter word with Q in it. Some examples are: quid, quad, quit, quip. quiz. qaid. qoph. quay. quod. quag.
Quit.
Iraq
Iraq
Iraq.
Iraq
Quit and qats (qat evergreen shrubs) are four letter word that start with q and ends with t. There are no four letter words that start with t and end with q.
There is only one four-lettered word that ends in 'q' - Iraq.
Dicq?
Cinq (five)
quad
quad, quid
Quij