Start to automate your own work where it is possible, if you want to run in automation.
QA can grow in several directions:
- test automation - for me, personally, it is boring - this is just a programming in test domain
- test design - creating new tests (not coding!) - crème de la crème of testing, as for me
- test management - manage test team, processes, test activities, test projects
I would also separate:
- test configuration management - creating and administrating test plants, beds, environments
- and test design and execution in performance testing - very interesting field, for my taste
Good luck in your choice!