Magnetism has been predicted to occur in systems in which dipolar interactions dominate exchange. We present neutron scattering, specific heat, and magnetic susceptibility data for LiErF4, establishing it as a model dipolar-coupled antiferromagnet with planar spin-anisotropy and a quantum phase transition in applied field H-c parallel to = 4.0 +/- 0.1 kilo-oersteds. We discovered non-mean-field critical scaling for the classical phase transition at the antiferromagnetic transition temperature that is consistent with the two-dimensional XY/h(4) universality class; in accord with this, the quantum phase transition at H-c exhibits three-dimensional classical behavior. The effective dimensional reduction may be a consequence of the intrinsic frustrated nature of the dipolar interaction, which strengthens the role of fluctuations.