  The competition between Kitaev and Heisenberg interactions away from half
filling is studied for the the hole-doped Kitaev-Heisenberg $t$-$J_K$-$J_H$
model on a honeycomb lattice. While the isotropic Heisenberg coupling supports
a time-reversal violating d-wave singlet state, we find that the Kitaev
interaction favors a time-reversal invariant p-wave superconducting phase,
which obeys the rotational symmetries of the microscopic model, and is robust
for $J_H<J_K/2$. Within the p-wave superconducting phase, a critical chemical
potential $\mu_c \approx t$ separates a topologically trivial phase for $|\mu|<
\mu_c$ from a topologically non-trivial $Z_2$ time-reversal invariant
spin-triplet phase for $|\mu|>\mu_c$.
