The concept of a new ultra-high resolution positron emission tomography (PET) brain scanner featuring truly pixelated detectors based on the LabPET II technology is presented. The aim of this study is to predict the performance of the scanner using GATE simulations. The NEMA procedures for human and small animal PET scanners were used, whenever appropriate, to simulate spatial resolution, scatter fraction, count rate performance and the sensitivity of the proposed system compared to state-of-the-art PET scanners that would currently be the preferred choices for brain imaging, namely the HRRT dedicated brain PET scanner and the Biograph Vision wholebody clinical PET scanner. The imaging performance was also assessed using the NEMA-NU4 image quality phantom, a mini hot spot phantom and a 3-D voxelized brain phantom. A reconstructed nearly isotropic spatial resolution of 1.3 mm FWHM is obtained at 10 mm from the center of the field of view. With an energy window of 250-650 keV, the system absolute sensitivity is estimated at 3.4% and its maximum NECR reaches 16.4 kcps at 12 kBq/cc. The simulation results provide evidence of the promising capabilities of the proposed scanner for ultra-high resolution brain imaging.