We develop the plasmon-pole approximation (PPA) theory for calculating the carrier self-energy of extrinsic graphene as a function of doping density within analytical approximations to the GW random phase approximation (GW-RPA). Our calculated self-energy shows excellent quantitative agreement with the corresponding full GW-RPA calculation results in spite of the simplicity of the PPA, establishing the general validity of the plasmon-pole approximation scheme. We also provide a comparison between the PPA and the hydrodynamic approximation in graphene, and comment on the experimental implications of our findings.