The present work explores the propagation characteristics of high power beam in weakly relativistic-ponderomotive thermal quantum plasma (TQP). Q-gaussian laser beam is taken in present investigation. The quasi optics equation obtained in present study is solved through well established WKB approximation and paraxial theory approach for obtaining 2nd order differential equation describing the behavior of beam width of laser beam. Further, numerical simulation of this 2nd order differential equation is carried out for determining the behavior of beam width with dimensionless distance for established laser-plasma parameters. The comparison of present study is made with ordinary quantum plasma and classical relativistic plasma cases