Rabbits in dreams usually represent fertility (specifically related to the earth, aka springtime) and sexuality. They are also luck charms, hence the existence of lucky rabbits' feet.
In the European tradition of dream interpretation, a black rabbit is a symbol of mourning. They can forecast a future death or represent grief over a recent death. This adheres pretty well to your experience.
In dreams, images manifest themselves as representations of subconscious desires and fears. It isn't that the rabbit itself is particularly scary; in dreams, innocuous symbols can take on an ominous meaning. It's that your subconscious has chosen to represent your fear of death in the form of a black and monstrous rabbit.
Knowing this, you can help conquer this fear - and put an end to your nightmares - by 'confronting' the entity in the physical plane. Draw it as best as you can, write a description, mold a model out of clay - whatever method you prefer, what's important is making a representative model with your own hands. Making it yourself represents releasing your fears into the object.
When it is finished, bury it or toss it into a body of water. This represents a total shedding of your fear. The act should prove very cathartic.
This is, of course, if you want to expel the creature. If it has provided you meaningful insight, it might be better to get to know it. Look into spells to contacting astral beings. The effigy you create will be useful for narrowing down the target of your contact attempt. Display it on your altar or hold it in your hand while you meditate.
Hope this helps! Blessed be.