Astrobiology is a field in biology more than in astronomy, though a background in astrophysics would be helpful. Studying extremophiles is likely the best background for astrobiology, as well as landscape ecology, or another field which studies biological processes by looking at emissions by biological entities.
The contribution of astrophysics to astrobiology is in figuring out the physical conditions on a planet, and testing for signals which could indicate life. The biologists are the ones who figure out whether life could exist in those conditions, and are the ones who try to figure out what are the signals that indicate life.
So, to be a astrobiologist, you will need to move to biology, and will require a strong background in biochemistry.
Good luck!