Is H1 B Filing possible on F1 visa before graduation

If I graduate in the month of May 2014 with Doctorate of Dental Surgery degree on F1 Visa status will I be able to file for H1 B visa on Aril 1st as I already finished my OPT period. I would like to know whether will I be able to work on H1 B visa from October as I will be graduating in May 2014. Will I be able to file for H1 B on 1st April if I graduate in May. Please advise.