MegatopLover, Just out of curiosity, how did you end up with a 36 hour connection in DOH given that they have 3× daily service to SIN (using 359s), unless it was an intentional stop, in which case it's not a connection.
If it's not a connection, you will likely be unable to check your bag(s) through from JFK.
FYI,
here's the HIA guide to what's allowed where, both arriving and departing.
Also, if you go to the HIA official website,
here, and use the magnifying glass at the upper right of that page to search on "lockers," you'll find a variety of references to the availability of lockers for bag storage, all of which seem to be airside. Don't know if that helps you at all.
Maybe if you call in advance and tell them that there will be a bottle of wine in your checked bag and you want to respect Qatar's law and tradition by not taking it into the country, they might consider allowing you to check it through. Just a thought. You don't have to identify yourself when you call, of course.