We investigate the structure of galaxies formed in a suite of high-resolution cosmological simulations. Consistent with observations of high-redshift galaxies, our simulated galaxies show irregular, prolate shapes with thick stellar disks, which are dominated by turbulent motions instead of rotation. Yet molecular gas and young stars are restricted to relatively thin disks. We examine the accuracy of applying the Toomre linear stability analysis to predict the location and amount of gas available for star formation. We find that the Toomre criterion still works for these irregular galaxies, after correcting for multiple gas and stellar components: the $Q$ parameter in $rm{H_2}$ rich regions is in the range $0.5-1$, remarkably close to unity. Due to the violent stellar feedback from supernovae and strong turbulent motions, young stars and molecular gas are not always spatially associated. Neither the $Q$ map nor the $rm{H_2}$ surface density map coincide with recent star formation exactly. We argue that the Toomre criterion is a better indicator of future star formation than a single $rm{H_2}$ surface density threshold because of the smaller dynamic range of $Q$. The depletion time of molecular gas is below 1~Gyr on kpc scale, but with large scatter. Centering the aperture on density peaks of gas/young stars systematically biases the depletion time to larger/smaller values and increases the scatter.
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