<p>This study explores how Rashba and Dresselhaus spin-orbit interactions affect the ground state properties of a two-electron system confined within a two-dimensional GaAs quantum dot, particularly under a magnetic field and Gaussian confinement potential. Using a variational approach based on a Chandrasekhar-type wave function with three adjustable parameters and a modified Jastrow correlation factor, we compute the interaction energy of the electrons with high accuracy under strong confinement. Key ground-state physical quantities such as interaction energy, magnetic moment, magnetic susceptibility, and chemical potential are analyzed. To assess the stability of singlet bound states, we construct phase diagrams for various realistic quantum dot parameters, showing how confinement strength controls electron pairing. The electron pair density function reveals spatial correlations between electrons and their evolution under different magnetic fields, dot sizes, and spin-orbit strengths. By analyzing the peak positions of the pair density distribution, we gain insight into the effective pair size in different regimes. Additionally, we calculate the average inter-electronic distance to quantify how the quantum dot environment shapes electron pairing behavior. These findings provide a deeper understanding of spin-orbit-driven electron correlations and the tunability of quantum dot systems for spintronic and quantum computing applications.</p>