  Using the constrained-path Monte Carlo method, a two-orbital model for the
pnictide superconductors is studied at half filling and in both the electron-
and hole-doped cases. At half filling, a stable $(\pi,0)$/$(0,\pi)$ magnetic
order is explicitly observed, and the system tends to be in an orthomagnetic
order rather than the striped antiferromagnetic order when increasing the
Coulomb repulsion $U$. In the electron-doped case, the $(\pi,0)$/$(0,\pi)$
magnetic order is enhanced upon doping and suppressed eventually, and a
$s_{\pm}$ pairing state dominates all the possible nearest-neighbor-bond
pairings. Whereas in the hole-doped case, the magnetic order is
straightforwardly suppressed and two nearly degenerate $A_{1g}$ and $B_{1g}$
intraband pairings become the dominant ones.
