Hello Konrad,
If i am not mistaken
The answer is it depends - Is your license is user based then No. (only 250$ /m for enabling Q)
If you have capacity pricing then Amazon Q question comes into picture and you need to have the Q&A pack ( basically min $500 you would spend) 250$/m for enabling Q and 250$/m for 500 Questions/m. Off course, you may go above this as well if you want.
FYI - I have capacity pricing and see my details as below
hope this helps and clears your doubt.
Cheers,
Deep