This thing isn't going to get 1G. No known power source could provide enough power-to-weight ratio sustained, and even if one could the engine would melt in seconds. Forget even 0.1m/s/s, and think thrusts measured in milinewtons.
That's not true. Using a matter/anti-matter annihilation drive, you can get to the nearest star at 1g acceleration with just 10 kg of fuel for each kg of payload. Now, it's true we don't have such an engine, but we do have (a tiny amount of) anti-matter, and the energy output is 100% efficient. So it's a known power source which can provide sustained acceleration with only about 10x the fuel to payload ratio, maybe a bit more to make up for a less than perfectly efficient thrust engine.