My 1 month old baby only seems to quiet down when I vigorously rock her (while I carefully hold her head). Can I cause her some (brain?) damage if I rock her too hard?
This really depends on what you mean by vigorously.
Shaken baby syndrome typically occurs with an unsupported head which is whipped back and forth. The damage is done by the brain being jostled in it's cranium.
If you are traveling at a specific velocity and reverse directions quickly, the brain will get jostled regardless of if it's held carefully or not. With repetition, yes, you can injure your baby.
Infantile colic begins at ~2 weeks of age and lasts for about 3 months. Talk to your pediatrician (or the nurse) to see if this might be the problem, and what you can do. Colic is common and extremely hard on the parents. You need some back up and some plans, perhaps even prescription probiotics to help the baby.
It's true that "babies don't break easily" but there is also a reason that infants are treated gently. There are lots of gentler ways to soothe a baby without risking her health. Though my first didn't have colic, I remember sometimes the only thing that would get him to stop fussing and go to sleep was to strap him into the car seat and drive aimlessly around. Bliss!