  Based on a minimal two-orbital model [Tai {\it et al.}, Europhys. Lett.
\textbf{103}, 67001 (2013)], which captures the canonical electron-hole-doping
phase diagram of the iron-pnictide BaFe$_{2}$As$_{2}$, we study the evolution
of quasiparticle states as a function of doping using the Bogoliubov-de Gennes
equations with and without a single impurity. Analyzing the density of states
of uniformly doped samples, we are able to identify the origin of the two
superconducting gaps observed in optimally hole- or electron-doped systems. The
local density of states (LDOS) is then examined near a single impurity in
samples without antiferromagnetic order. The qualitative features of our
results near the single impurity are consistent with a work based on a
five-orbital model[K. Toshikaze {\it et al.}, J. Phys. Soc. Jpn. \textbf{79},
083704 (2010)]. This further supports the validity of our two-orbital model in
dealing with LDOS in the single-impurity problem. Finally, we investigate the
evolution of the LDOS with doping near a single impurity in the unitary or
strong scattering limit, such as Zn replacing Fe. The positions of the ingap
resonance peaks exhibited in our LDOS may indirectly reflect the evolution of
the Fermi surface topology according to the phase diagram. Our prediction of
ingap states and the evolution of the LDOS near a strong scattering single
impurity can be validated by experiments probing the local quasiparticle
spectrum.
