No you wouldn't have to check it. Domestic flights don't have the same LAGs restrictions as international flights do.
AFF Supporters can remove this and all advertisements
I would not put it in my bags to go under the plane as all your clothes will have a little bit of alcohol content
I think there is a limit to the amount you can bring onboard, but as stated you don't have the same LAG issues as what you do flying out of an international terminal.
FWIW - clothes can do a very good job in protecting bottles or glass that does get checked.