Suppose I have a space ship that can accelerate to c in one month of acceleration/deceleration of month and I want to travel to Andromeda. From my frame of reference wouldn't my total travel time be two months?
You may want to see The Relativistic Rocket [1] for details on how to calculate this and what the results are. [1] http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
Assuming this means "very, very close to c": 1 month in which system? For the ship: then sure. For earth? Then the ship will experience even less time.