Just visited the XDA developer website forums and found that a custom ROM for Galaxy Tab P1000 already available. The CyanogenMod 11.0 custom ROM, built and compiled by terenceng, I just downloaded the ROM and flashed to my Galaxy Tab P1000 via CWM Recovery.

UPDATE: There is unofficial release of CyanogenMod 13 which is based-on Android 6.0 Marshmallow available to download. You can follow our tutorial on how to install CyanogenMod 13 on Galaxy Tab P1000.