Submission of your state license is a requirement for filing the H-1B petition. You should allow yourself plenty of time to apply for a license in the state in which you intend to practice. You should do this while you have plenty of time left in J-1 status so that you can obtain a permanent license. If you obtain a temporary license with an expiration date USCIS may only grant your H-1B up until the date your license expires.
For help with your immigration issues call us at 415-986-6186 to schedule a consultation. You can also always visit my website at: www.doctorsimmigrationlaw.com where we have free articles and resources to help you.