Extended, old, and round stellar halos appear to be ubiquitous around high-mass dwarf galaxies ($10^{8.5}<M_star/M_odot<10^{9.6}$) in the observed universe. However, it is unlikely that these dwarfs have undergone a sufficient number of minor mergers to form stellar halos that are composed of predominantly accreted stars. Here, we demonstrate that FIRE-2 (Feedback in Realistic Environments) cosmological zoom-in simulations are capable of producing dwarf galaxies with realistic structure, including both a thick disk and round stellar halo. Crucially, these stellar halos are formed in-situ, largely via the outward migration of disk stars. However, there also exists a large population of non-disky dwarfs in FIRE that lack a well-defined disk/halo and do not resemble the observed dwarf population. These non-disky dwarfs tend to be either more gas poor or to have burstier recent star formation histories than the disky dwarfs, suggesting that star formation feedback may be preventing disk formation. Both classes of dwarfs underscore the power of a galaxys intrinsic shape -- which is a direct quantification of the distribution of the galaxys stellar content -- to interrogate the feedback implementation in simulated galaxies.