If you are fearful about coming into Headstand without your teacher, I advise starting at a wall. Use the wall to stabilize your pose and build confidence in the inversion. Over time you may remove your legs from the wall, one at a time, to learn to balance. But don't be in a hurry to free balance because you will risk compressing the vertebrae in your neck.
Entering any inversion requires strength from the abdomen both as you move into the pose and to stabilize you while you're in the pose. When you come into Headstand by yourself, you won't actually "kick up," you will draw your legs over your head by drawing in and up on the navel center, thus engaging the abdominal muscles.