You can do that. I used to do a bit of running, but dont really bother anymore, but I cant imagine anyone not being able to do 10k (obv thats just me lol)

I would suggest that every time you train, you do 10k. Even if its just fast walking with a bit of running thrown in.

I dont like to run on a treadmill so it might be easier for you to run outside. Do some interval training too, jog for a bit, sprint for a bit etc to build up your stamina.