time on feet and base building is so important. I recommend doing 3-4 slow runs a week where you stay in your heart rate zone 2 or 3 max. On one run make sure it’s a longer run and keep pushing yourself on distance each week until you can handle a half distance at that slower speed. 

That sounds a bit like my first half marathon, got egged on by a co-worker and we had 6 weeks to train!

I'm going to echo @RonC with time on feet and base building, get 90 minute and 2 hour long runs in. As you're going past 2 hours at high effort you need to think about refueling or those last 5k will be very hard. Start practicing gels, isotonic drinks etc 

Your easy runs should be slow, check your HR for the right range but the rule of thumb is if you can have a conversation then thats the right pace.  

Once you can handle the distance then add an interval session once per week, this will get your speed up.

Hello

Its already been said but base work is key! 
Lots of Zone 1 and 2 to work to build aerobic capacity. Get used to be on feet for 2 plus hours and understanding how it feels to be out for that long and definitely start to think about how you fuel it. 
Personally I wouldn’t fuel for any run under an hour, but when I am fuelling I think about getting fuel in early, so from 30mins onwards. 
The key is to safely complete your first half marathon and learn from it. Don’t get hung up on the finish time, just aim to complete and enjoy it! 
If you can run a 10K already, then building to 21K for December won’t be difficult, just built the distance gradually over the coming weeks to avoid injury and you’ll be golden! 

Yeah, people have hit the main points already, but I figured I could toss in my two cents.

Don't get fall into the "I'm going too slow" pit. I've been lucky so far and never really suffered any major injuries, but the few times that I've hurt myself and had to take some time off to heal it has always been because of pushing myself too hard. 

Remember that you shouldn't increase your weekly distance by much more than 10% (e.g. if you run 50k a week, then you should only really up that to 55k the next) and that the vast majority of your training should be done at low-effort. What I (and most runners) find helpful is to plan out your runs and have set workout days. If you haven't done much dedicated training, start with just 1 day a week of actual training (e.g., stuff like running intervals, high-effort runs, etc.) and 1 long run a week. Everything else should either be rest or easy runs. And by easy I mean EASY. I'm not the fastest dude in the world, but I'm still pretty proud of my pace. My full-marathon pace is around 4:30/k, but my easy pace is around 6:00/k. Slow way, way down for easy runs.

My general advice for runners is that you should be able to do your entire easy run without mouth breathing. Breath through your nose! If you start getting short on breath, slow down and gulp some air. Then, back to nose-breathing.

And, finally, don't neglect speed work! Long runs and endurance stuff is definitely important, but dedicate some time to running 400 and 800m intervals! First, they are fun and let you stretch your legs. More importantly, though, they help you go fast and push your fitness. You think that running a half should be all about going long, but if you get used to pushing through some intervals your body will be more adept at recovering  from efforts. That means you'll be able to maintain your pace over longer periods of time.

Hey @nethuliruns8 I was curious and wanted to follow up and ask how your half marathon last month went for you? What were your biggest takeaways and what did you learn?