Hi! Im not an expert but i hear that running on the treadmill isnt a good form of regular training for road running because you arent actually doing much work yourself as the treadmill is the thing thats moving at speed, all you have to do is simply move your feet in time and dont need to push off with your feet to go forwards. Know what im trying to say?
i wouldve thought that is why when you went out to run on the road, the time you could run constantly for was decreased quite significantly. I find the treadmill is good for practicing speedwork and things but really getting out there and practicing on the roads is much much better and more beneficial.
keep up the motivation and keep going out and running on the roads!
ps, i did my first half marathon back in April and had only been running for about a year before hand. The most id ever ran on the roads was 7 miles.....a week before i was to do it!!!
So, yes. With regular training a half marathon will be achievable by October. And you'll probably be quite surprised by what time you run it in too!!! Good luck in advance on that one!