I would start working on getting the medical license ASAP. Some states are notoriously slow and inefficient with getting you the license. NJ, California & Florida in particular have reputations of driving doctors bonkers with the process. In NJ, you'll have to wait 6-12 months before they approve your license, and pay a hefty fee (about $1000). In Pennsylvania which is NJ's neighbor, and was right across the river, it took about a month, and was extremely cheaper vs NJ with the fee.
Some places won't even consider you until you get the license. After you've obtained one, I would start calling places at least a few months ahead graduation. The sooner the better, but at this point I wouldn't worry.