The purpose of this work is to develop a validated Geant4 simulation model of a whole-body prototype PET scanner constructed from the four-layer depth-of-interaction detectors developed at the National Institute of Radiological Sciences, National Institutes for Quantum and Radiological Science and Technology, Japan. The simulation model emulates the behaviour of the unique depth of interaction sensing capability of the scanner without needing to directly simulate optical photon transport in the scintillator and photodetector modules. The model was validated by evaluating and comparing performance metrics from the NEMA NU 2-2012 protocol on both the simulated and physical scanner, including spatial resolution, sensitivity, scatter fraction, noise equivalent count rates and image quality. The results show that the average sensitivities of the scanner in the field-of-view were 5.9 cps kBq-1 and 6.0 cps kBq-1 for experiment and simulation, respectively. The average spatial resolutions measured for point sources placed at several radial offsets were 5.2 0.7 mm and 5.0 0.8 mm FWHM for experiment and simulation, respectively. The peak NECR was 22.9 kcps at 7.4 kBq ml-1 for the experiment, while the NECR obtained via simulation was 23.3 kcps at the same activity. The scatter fractions were 44% and 41.3% for the experiment and simulation, respectively. Contrast recovery estimates performed in different regions of a simulated image quality phantom matched the experimental results with an average error of -8.7% and +3.4% for hot and cold lesions, respectively. The results demonstrate that the developed Geant4 model reliably reproduces the key NEMA NU 2-2012 performance metrics evaluated on the prototype PET scanner. A simplified version of the model is included as an advanced example in Geant4 version 10.5.