Been there, done that, several times
If your company is large enough, see if you can transfer to another team or project where you wouldn't be reporting to this person.
If not, start looking around. Definitely have a new job lined up, with an offer letter and a firm start date, before you give notice. But be patient - the job market is still pretty bleak. It'll also look strange that you were at your present company for only 1 month. Many companies ask your reason for leaving, and you'll need something more solid than "I don't like my boss" - that makes you sound like you're not a team player. You could say "poor opportunities for promotion/advancement" or something like that.
Good luck
