The most logical career path for a teacher is to start out as a classroom teacher, then perhaps take on some additional roles like achievement leader or head of the house. After this, you might be looking for a bigger promotion, like a promotion to the position of running your department. As a head of a department, you will have a lot more responsibility, so you need to show that you can handle it.
There are no specific qualifications that you will need, though it will help you to have additional qualifications, like an MA in education, perhaps. This will help you to stand out from the crowd and will show your commitment to teaching.
You should also consider your involvement in the school as a whole. Make sure people know who you are and what you are capable of. Take part in general school life and offer to help out with things like assemblies to show willing.