Opt Validity and Driver's License renewal


I am currently on my 12 month OPT (ends on 08/29/2014) with an approved H1-B which starts from 10/01/2014. Because of H1-B approval my employment authorization has been extended to 09/30/2014 (as per the new I20 issued by the university). My driver’s license is valid only till 08/29/2014 which is same as mentioned on my OPT card. Please let me know if I can renew my driver’s license with my new I20 and other H1-B approval documents? If yes, will it be valid till the date mentioned on I20 (09/30/2014) or beyond that? Or do I need to apply for STEM extension to do so? Or do I need to complete the process of H1-B stamping to be able to renew?

Thanks a lot in advance!