H1 APPROVED FOR FY2014, CAN I CHANGE EMPLOYER AND HAVE MY H1 TRANSFERRED?

I am on H4 visa in USA right now, my H1 is approved for FY2014. As i can start working only from oct 2013, can i change my employer now ,that is before oct 2013 and transfer my H1B to a new employer and start working directly for the new employer in oct 2013.

Has anyone done this before or has any information about this? plz let me know if its a safe option? I dont have any contract with the employer who did my H1B.

Thank you.

Another employer can file cap-exempt petition for you w/ COS and start date of Oct 1. Once you have finalized the employer, you can check w/ their attorney as well.