OVER MY HEAD?

Ok so is it even realistic to think 6 and a bit months is enough time to train for a half marathon? Like to run the whole time without having to walk any of it? Because that is the goal!! To actually run the whole thing. I know I can run 13k but it takes me FOREVER!! And it doesn't help that it's still winter out there. I don't care what anyone says running on a treadmill is not the same as running outside! Starting to freak out a bit here...