The 10 mile difference will take a toll on your body when you compare the 3.1 mile and 13.1 mile races together, but in actuality, the human body is capable of storing enough energy to run for 20 miles (but don't run as fast as you can, expecting to run at that speed for a half-marathon). This means that once you get your body in a rhythm, your half-marathon isn't just a dream. Getting into the groove for a 3.1 miler can easily transfer to a 13.1 mile race... but it takes steps in order to get there.
A simple rule of thumb that has been said over and over is the 10% rule. Your weekly miles should not increase more than 10% per week. For example, if you run 10 miles a week, if you strictly follow that rule, the weeks will go by like this: 10, 11, 12.1, 13.31, 14.641, 16.1051... and so forth. If you run 20 miles per week, it would go like this: 20, 22, 24.2, 26.62, 29.282, 32.2102... and so forth. If you look at the six weeks, you can see the progression exponentially increase. The purpose of this 10% rule is to insure that the individual will not get injured. However, I believe that the rules are more like... guidelines. To me, I don't follow those rules strictly because rules can be confining. Most runners have the problem of confining themselves and giving themselves limits. However, each day, everyone feels different. We have our good days, our bad days, our busy days, our free days, and because of that, I think it's not wise to limit ourselves because of our set 'schedule'. Instead, we ought to keep the guidelines in our heads and work towards a positive progression, making sure to know our bodies, and push it in a positive manner, rather than pushing too much and getting ourselves hurt or pushing too little and not reaching our full potential.
It's good to create goals and have every little detail about the steps you take towards your goal, but my suggestion is to think outside the box and allow adjustments to happen... sometimes even during the run, and work towards your goal, always making sure that each step is the best thing for the goal. Keeping the goal in mind means that adjustments are mandatory. Whatever your goal may be, you need to make sure that you don't get caught up in the 'rules' and instead, enjoy the training, and enjoy the freedom.
When you train for your half-marathon, my advice is to run slow, and run long. Don't worry about speed because in time, speed will take care of itself. Unless you are an elite athlete, ease into it with your long runs, and make it your goal to not stop during the race. With that goal in mind, take steps forward and run far, run easy, enjoy the weather, get a tan, focus on just clearing your mind... and before you know it, you'll be able to run a half-marathon.
I remember my first (and only) half marathon. We had our cross country championships in Guam with all the other International schools in the Far East. Friday was our individual race and Saturday was our relay. Sunday, there was a PIC International 5k/10k/Half-Marathon, and two other guys and I thought it would be fun to try it out. We signed up and when the race started, we started out slow, because we had never run this far before. We were just High School Cross Country runners with no experience running long distances. Because of my fear of bonking out from running too fast, I was able to do really well and finished 10th overall with a time of 1:37:23, an average of 7:26 min/mile, 1st in my age group. I was given the honor of shaking Frank Shorter's hand as he gave me a trophy for winning my age division. The rest of the day, I was in pain because my legs had never felt 13.1 miles of racing before. I was happy, but it hurt a lot. My resolve to continue through the tough times really helped me during that race, and although I did not train for the race, being able to run a good 5k definitely helped me with my half-marathon.
My training for the 5k included long runs which was only 8 miles, which helped my stamina as I pushed hard for a 3.1 mile race, but without knowing, training for a good 5k time actually improved my half-marathon time. My speedwork for the 5k transferred over to the 8 mile long runs, which in turn helped me out with the half-marathon. Everyone is different, but running still requires the same principles. Some of your runs will be long and easy to improve your endurance, and others will be short and fast to improve your speed. Combining the training will make it so that you could do your best. 5k to half-marathon is a lot easier than you think. Run smart, and keep the guidelines in your head.
This morning, I worked on my slow race pace and ran 3.28 miles in 30:54 (9:24 min/mile average) and in the afternoon, I worked on my cadence and ran 6.98 miles in 51:41 (7:08 min.mile average). It was a good day.
(side note... I'm pretty sure that my iPhone's running calculator is slightly off in calculations... but I'm just going ahead and putting it on. I was certain that I finished the run in less than 50 minutes... so the 7:08 average actually makes more sense... but it's just a training run, so it's no big deal)