It meeds careful meshing and selecting the time widow for post processing.
The uniform mesh is to guarantee the periodicity. Without proper periodicity the result might deviate the theory. Please note that the discrete mesh matters for the simulation.
As far as 2008 Harvard team reported over 1M Q factor for Photonic crystal cavity so high Q is not an issue for Lumerical FDTD.
Once the meshing is proper, both the dipole sources and the time monitors can be modified to be placed where the field intensity is strongest for around the desired wavelength. You can place one or more profile monitors to record the fields with much longer simulation time than Q simulation, with apodization setting:
Thus it will be iterative: get rough resonant wavelength and Q, modify the locatios of the dipoles and time monitors, simulate Q again,... when the mesh is proper. Please note in the two cases the simulation time can be very different.