Congratulations on the certificate. Yes you do need the compass and the correction card goes with the compass. Here is the Part 91 requirement:
FAR 91 aircraft equipment required
Day VFR minimum equipment: airspeed, altimeter, compass, tachometer, fuel gauge, oil temperature, oil pressure, (gear indicator and manifold pressure)
Night VFR minimum equipment: Position lights, beacon, power source, and a flashlight. Class D airspace requires a radio while Class C and B requires radio, and an encoding transponder.
Transponder required above 10,000' in TCA, in ARSA, and above ARSA. FAR 91.413 requires the transponder to be checked and certified within the preceding 24 calendar months.
You are almost there!