This paper introduces GLAAPE, a novel graph learning assisted neural network model that enables fast, accurate, and transferable estimation of average power in RTL designs from RTL simulation without the requirement of gate-level simulation. GLAAPE learns to propagate the toggle rates by effectively em- bedding logical function feature values as vectors on each logic cell of the netlist file. We evaluate GLAAPE with a commercial gate-level power estimation tool for inference throughput, commercial RTL power estimation tool for average power estimation and state-of-the-art model GRANNITE for predicting toggle rates and show a mean improvement of 15.69X, 25.28% and 13.95% respectively.