A
singularity or a
black hole is not essentially
quantum in nature. Black holes are described in
General relativity and other theories of
spacetime and
gravitation (such as
Dynamic Universe), with no regard to
quantum mechanics.
There is not any generally accepted theory that combines general relativity with quantum mechanics (i.e. quantum gravity). However, when dealing with black holes properly you would need one, because the small dimensions involved suggest that quantum effects are significant.