Is this a trick question.

How often have you travelled into Doha Airport?????

Does Doha Duty Free have a counter selling Alcohol while entering Qatar????????

I have never seen it..

Since there is no counter selling Alcohol while entering Qatar, you can't buy it, unless you bring it from abroad, in which case, no.

I am sure, Qatar Airways, or any other airline will advise you in the aircraft, that Qatar is a country that does not allow the import of alcohol.