Plenty of time. My first HM, I started from a base of running four miles, three times a week. I then followed a very simple schedule I found online (http://www.marathonrookie.com/half-marathon-training.html) - scroll down the page for the schedule, and there's a printable pdf version linked as well. It takes you up to 1 12 mile training run, although I went a bit further - psychologically, I found it helped to have reached and passed 13 miles in training, so that on the day, when I was trying to run it, I knew I could make the distance - it was the time that was the challenge. There are lots of other, more structured plans available, involving speed sessions etc.
Remember that your longest run each week is an LSR - long slow run. That means it should be run at a conversational pace (you could chat with someone). It would also be beneficial to run at least one run a week (preferably not the one just after your LSR) at a good speed (for you).
Since you have time, I'd suggest building up to something like the weeks 5-7 of the scheduleI indicated, then either alternate hard (that level) and easy (drop yourlong run down by two or three miles) weeks, or do two weeks hard (e.g. weeks 6 and 7 of this schedule) then one week easy. That way you should get your legs ready but not too tired. Also, you've got time so if you get a cold, or a niggle (e.g. a pulled hamstring) and can't run for a week, it won't be important.
If you have a parkrun nearby (look it up - free, timed 5K runs in parks all over, every Saturday - just register online, print your ID and turn up), go do that sometimes as weel - they're fun and friendly.
Tapering the last couple of weeks should have you itching to get out there and run the half!
And, most importantly, enjoy! Enjoy the training runs and you'll enjoy the HM.
