Six months. You can totally do it.
I trained for a 1/2 marathon in about 4 months time... but I was also training for a 1.2 mile swim and a 56 mile bike before the 1/2 mary.
I also couldn't run the last month before my Half Ironman... so I went into a 1/2 mary without even running the month before. Mind you, I walked most of it, but I was fine with that.
So yea... you can do it! GO FOR IT! Good luck!
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"