Legal options to collection rent when tenant moving out one month before lease expiration?

[Kazi R.]

I have this tenant (in GA) whose lease is expiring on Mar 31 of this year, but just got a notice from her that she will be moving out at the end of Feb and asked me to accept security deposit for March rent, which I absolutely don't agree to do. This is someone whom I gave good references to help find another place. What are my legal options to collect the rent for March? Should I file for eviction once the due date for March rent has passed? I have never dealt with a situation where tenant is moving out one month before lease expiration, so any help will be greatly appreciated. Thanks.