I'm not aware of "to head off" meaning "to disturb"! It can mean to cause something to change direction or course, to put it off its original planned direction.
However, here it simply means "to commence a journey" or "to leave your current location".
It's time for me to head off now. I have a job interview to get to.
My parents came to visit yesterday. I thought they would never leave but they finally headed off around 9pm.