A few days short of a year being 354 days. You can get a pretty long way in a year, assuming my calculation isn't wildly off. You'd need plenty fuel, I don't intend to calculate how much.
The amount of fuel you would need would be infinite to reach the speed of light because as it approaches the speed of light its mass increases to infinite at the speed of light. It therefore requires more and more energy and therefore fuel to maintain the constant 1G acceleration as you approach the speed of light until the energy required to actually reach the speed of light becomes infinite.