Why do you want to do a half marathon? Just to finish it and say you've done the distance? Since you've been working up to the distance and have a desire to run races, it seems that running the whole way and doing the best that you can do would be more your goal than just finishing.
Almost everyone on here is going to tell you that Galloway's advice is "full of beans". But almost everyone on here wants to compete, not just finish. Since you're a beginning runner, competing for you doesn't mean that you have to be in the fastest group going for the win, but that you run to the best of your ability. Your dedication in training so far proves that your best is more than walking.
I suggest two things if you're able to- do a weekly group run with the local running club- there are runners of all abilities and you often find yourself running faster and longer with less effort because you don't have the entire burden of keeping the pace. Secondly, if you have access to a pool, use it for cross-training if running more is starting to stress your body. You won't get injured from a race if you're properly prepared, and walk breaks during a race won't save you from injury. As you're building up running mileage and lengthening your runs, the pool is a good way to get in exercise with low impace.