Yes, you immediately fall out of status if you quit your job. Even though you may not be unlawfully present, if your I-94 is still valid, you will be out of status and even if you find another job, you will not be eligible for a H-1B transfer if you are no longer in valid H-1B status. You would have to go abroad for consular processing.
Answered on Jan 24th, 2013 at 1:13 AM