  We characterise the properties of a vortex line in an elongated dipolar
Bose-Einstein condensate. Increasing the strength of the dipole-dipole
interactions (DDIs) relative to the short ranged contact interactions we find
that the system crosses over to a self-bound vortex droplet stabilized from
collapse by quantum fluctuations. We calculate the quasiparticle excitation
spectrum of the vortex state, which is important in characterizing the vortex
response, and assessing its stability. When the DDIs are sufficiently strong we
find that the vortex is dynamically unstable to quadrupolar modes.
