In this work, we have developed analytical models for the channel potential, threshold voltage and drain current for a cylindrical Gate-All-Around Junctionless Metal-Oxide-Semiconductor Field Effect Transistors (GAA-JLTs) with Gaussian doped channel region along the radial direction with uniformly doped source and drain regions. It has been found that the variation in doping parameters, such as, straggle, projected range and peak doping concentration, significantly affects the device characteristics such as threshold voltage, Ion/Ioff and so on and therefore, tuning them may bring about optimized device design, avoiding excessive leakage current yet maintaining high on-state current. The results obtained through our proposed analytical model are validated by ATLAS 3-D device simulator. Further, the variation of channel potential with doping parameters and bias potentials have been investigated. We have shown that by tuning the doping profile parameters together with the aspect ratio (AR) of a non-circular cross-sectional JLT, the threshold voltage and Ion/Ioff can be optimized along with reduction in DIBL. The effects of Gaussian doping on few figures-of-merit (FOMs), as applicable to analog domain, have also been analyzed. Computations with necessary discussions have been presented to explore the impact of key doping parameters on the linearity of GAA-JL devices.