I don't see why you should'nt do that one as well. If it were me, I'd definitely do both. Depends on just how you feel after the first one. Hopefully it won't be too traumatic (physically or mentally), and you should have recovered sufficiently in the time between the two races.
Month would be fine... I did 2 halfs 14 days apart last year, and although I was pushing myself to go faster in teh second, I seemed to struggle with it more... I certainly felt like I wasn't fully recovered, and heavy legged from the first half - A month should be absolutely fine though
Not trying to go one better or anything Richard but I did 2 last year a week apart and pb'd on the second, I ran both at my race pace, but on the first one the elements were very much against me wind, rain hail you name it, it came down and I wasn't happy with the time I did and so I ran another a week later although I pb'd again I still didn't hit my target, but I will next time. I hope
I would just like to add this isn't something I would recommend to anyone, like Richard says it's down to the individual.
That could well be the case - I would've thought 2 weeks should be enough time to recover, and i've never been sure if it was the previous half mara, or the fact that I was running at an increased pace that destroyed me in the second attempt.
It's all down to the individual as well - like those maniacs who manage marathons day after day after day - mental!