We report results of simulations of the $2+1d$ Thirring model
with $N$ fermion flavors,
defined on a lattice using domain wall fermions. This approach is devised to
respect as far as possible the underlying U($2N$) symmetry of the continuum
model, expected to be recovered in the limit wall separation $L_s\to\infty$. For
$N=1$ there is a symmetry-breaking phase transition associated
with bilinear condensation at strong fermion self-interaction, which is a
plausible location for a quantum critical point. Fits to a
renormalisation group-inspired equation of state yield critical exponents distinct from those obtained using a version of the model defined using staggered fermions.