We demonstrate simple and robust methods for Doppler cooling and obtaining high fluorescence from trapped 43Ca+ ions at a magnetic field of 146 Gauss. This field gives access to a magnetic-field-independent 'atomic clock' qubit transition within the ground level hyperfine structure of the ion, but also causes the complex internal structure of the 64 states relevant to Doppler cooling to be spread over many times the atomic transition line-width. Using a time-dependent optical Bloch equation simulation of the system we develop a simple scheme to Doppler-cool the ion on a two-photon dark resonance, which is robust to typical experimental variations in laser intensities, detunings and polarizations. We experimentally demonstrate cooling to a temperature of 0.3 mK, slightly below the Doppler limit for the corresponding two-level system, and then use Raman sideband laser cooling to cool further to the ground states of the ion's radial motional modes. These methods will enable two-qubit entangling gates with this ion, which is one of the most promising qubits so far developed.