Or you could say "저 오늘 머리 하러 가요." This is more like "I'm going to change my hair style, today."

you can either say 저 오늘 머리 깍아요. or 저 오늘 머리 잘라요. The second expression is meaning as 'I m cutting my head off.' I know this is kinda weird but since there is no one cutting their head off themselves, we understand that it means 'I am getting a haircut.' by the way, when you pronounce those words, it goes like this 깍아요 [까까요] --> [저 오늘 머리 까까요] 잘라요 [짤라요] --> [저 오늘 머리 짤라요]