You can file H1 application during 60 days grace period.
If your grace period will expire before Oct.1st, you have to use quota of 2005 for graduate degree got from US, otherwise you may be required to leave to apply visa even if your transfer H1 from F1 is approved;
If your grace period will expire after Oct.1st, you can use quato of 2005 or 2006 for graduate degree got from US.
you have to pay attention to the quota while you are looking for job offer.