You can only be granted H-1B status as of October 1, 2013 and will have to maintain your status until then or leave the US upon the expiration of your current status. Filing an H-1B petition will not keep you in status. Moreover, time spent in L status will counted towards H-1B term.
If you find an H1b petitioner, they can file for you on April 1, 2013.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.