Training for a half marathon

So I started training for a half marathon last week. A friend has convinced me to run in his yearly group run that's right at 13.1 miles. Since that is considerably farther than a 5k or 10k, I can't just show up the day of and run like I have my last 2 or 3 races. And besides, the regular running is good for me.
I started last week and ran a 5k on 3 different days. This week so far I've run 3.5 miles on Monday and early this morning. I plan on running 4 miles this Saturday. My plan is to run 3 or 4 miles for 2 days and then increase my longer run on the 3rd day. So this week is 4 miles. Next week will be 5, the week after 6 and so forth. The half marathon is on October 2nd.
I hope to be up to 9 or 10 miles and the thought is what's another 3 or 4 miles. We'll see how that works out.
Also of note, on September 17th is the Raider Run. It was last year's Raider Run that was my first race ever. I'm excited to do that one again and see how different it will be this time. I'll be able to run the whole race this time around as well as improve my time by at least 10 minutes.
I'm still maintaining my weight. I'm in that 225 to 230 pound range.
I keep thinking that I'm in over my head on this half marathon deal but then I remember a few things. Up until last year, I never thought I'd run a 5k. Up until a few weeks ago, I never thought I'd run a 10k. So why can't I run a half marathon. I'm the only person standing in the way.