A treadmill is a very good place to gain stamina, but only 1km is very little.
Suffice to say, if you want to complete a half marathon, you won't be running 1km per day, and then suddenly 21km on event day, right?
If you run on a treadmill you have the luxury of setting a steady tempo for yourself, and seeing how far you can get at that tempo without having to walk.
So one plan of attack would be to set the treadmill to say 12km/h, and test yourself. Say you can run 8km at that pace, you have a benchmark to go by.
After a month of running at different speeds and different distances, try testing yourself at 12km/h again.
You should also seek to test yourself at distances outside, in the environment that the half-marathon would be held on (concrete, terrain, etc). Try for instance completing a 10k as fast as you can, and use that as another measurement for your progress.
Calculating your needed average velocity
Say you want to complete the half-marathon in 4 hours (just an example).
21km / 4h = 5.25 km/h, so that's the average speed you'd need to complete it in that time. I see now that this should be a very pedestrian speed, so let's try 3 hours.
21km / 3h = 7km/h. This should be very doable for most people, especially someone who is already presumably in decent shape.
You get the idea, right? You should easily be able to gauge whether or not you'd like to participate in the upcoming half-marathon based on what you've been seeing on the treadmill.