We numerically study supercontinuum (SC) generation (SCG) in a rare-earth-doped highly nonlinear photonic crystal fiber (HNL-PCF) with anomalous dispersion (AD) in the sub-picosecond pulse regime. We develop a semi-classical numerical model based on the generalized Ginzburg-Landau equation in order to take account of ultrafast interactions between gain ions and ultra-broadband SC radiation encompassing sub-100femtosecond solitons. Based on the numerical model, we analyze SCG characteristics of an active HNL-PCF in comparison with a passive-type counterpart, unveiling novel optical gain effects in a highly nonlinear optical fiber with AD. We rigorously investigate gain-induced soliton dynamics, such as soliton-cascadelike behaviors, soliton-quasi-soliton collisions, and phase-matched dispersive wave generation, which eventually contributes to enhancement of energy scaling of SC radiation without incurring considerable degradation of its spectral flatness. We also verify that such superior performance characteristics of an active HNL-PCF make it suitable for the use as a boost amplifier for SC radiation. We think that the findings from this study will incite other subsequent studies on unveiling detailed nonlinear pulse dynamics in various gain-embedded nonlinear optical media.