  We consider disk stability in the quasi-linear formulation of MOND (QUMOND),
the basis for some $N$-body integrators. We generalize the Toomre criterion for
the stability of disks to tightly wound, axisymmetric perturbations. We apply
this to a family of thin exponential disks with different central surface
densities. By numerically calculating their QUMOND rotation curves, we obtain
the minimum radial velocity dispersion required for stability against local
self-gravitating collapse.
  MOND correctly predicts much higher rotation speeds in low surface brightness
galaxies (LSBs) than does Newtonian dynamics without dark matter. Newtonian
models thus require putative very massive halos, whose inert nature implies
they would strongly stabilize the disk.
  MOND also increases the stability of galactic disks, but in contradistinction
to Newtonian gravity, this extra stability is limited to a factor of 2. MOND is
thus rather more conducive to the formation of bars and spiral arms. Therefore,
observation of such features in LSBs could be problematic for Newtonian galaxy
models. This could constitute a crucial discriminating test. We quantitatively
account for these facts in QUMOND.
  We also compare numerical QUMOND rotation curves of thin exponential disks to
those predicted by two algebraic expressions commonly used to calculate MOND
rotation curves. For the choice that best approximates QUMOND, we find the
circular velocities agree to within 1.5% beyond $\approx 0.5$ disk scale
lengths, regardless of the central surface density. The other expression can
underestimate the rotational speed by up to 12.5% at one scale length, though
rather less so at larger radii.
