"The rabbit drinks milk."
Translation:Tavşan süt içer.
Nope, subjects are never in the accusative case. It is only for direct objects and a few time expressions.
There is no way to distinguish "a rabbit" and "the rabbit" when they are subjects (unless you choose to include "bir" in front of it).
Read this carefully to learn more about the accusative: https://www.duolingo.com/comment/7738396