Approx. 1G is about 10m/s per second. The speed of light is 300,000,000m/s. Therefore it will take 300,000,000/10 or 30 million seconds to get to the speed of light. Which equates to about 350 days or one year. Since the acceleration is constant from zero to the speed of light the distance travelled in a year will be about half a light year. More precisely the distance travelled is s=0.5a.t². a= 10m/s², t=30,000,000 so s=4.5.10¹⁵m or just under half a light year as expected.
I'm not exactly a brainiac but remembering a bit of school physics- I can remember equations of motion at least- I make it a few days short of a year. There's probably all sorts of relativistic shoot that says my answer is bollocks though.