You have a 30-day grace period for J-1. To recommend a course of action, one would need more details - such as would your H-1B start Oct 1, 2013, or sometime sooner. In other words, will you have a gap between J-1 expiration and H-1 start date? Might not be a bad idea to consult an immigration lawyer privately.
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I agree with my colleague. Generally you have a 30 day grace period at the expiration of your J-1. When does your H1 start.? My best advice is to consult an immigration attorney.
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You only have a 30 day grace period, which means you will need to leave the US, obtain an H-1B visa in September, and return with that visa in order to be in H-1B status.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.