[1]> According to wikipedia, interstellar travel at 1G would take approximately 1 year + the distance in lightyears. Proxima Centauri (4.2 light years) for example would take 5.2 years.

This^ is from the traveller's standpoint. I am not completely sure about how long it would take from the perspective of someone on Earth. But this definitely seems plausible if we can solve the other problems with constant acceleration such as sufficient fuel and protection from interstellar dust (at close to light speed, dust would hit with unimaginable force).

[1] https://space.stackexchange.com/questions/840/how-fast-will-...