Yes the MOS would be 11B1P, the "P' being the Special Qualification Identifier (SQI) indicates "parachutist".
The U.S. Army changed the MOS coding structure sometime in the 1980s, so this MOS code is now part of history. While MOS codes can be useful especially when visiting the Wall or searching through the casualty database, they can be fairly hard to find these days.
A United States military occupation code, or a Military Occupational Specialty code (MOS code), is a code used in the United States Army and United States Marines to identify a specific job. In the U.S. Air Force, a system of Air Force Specialty Codes (AFSC) is used.
Check out the complete list of army enlisted MOS's at Thebalance.com.