The Black Dog is the name given to a folklore creature, which is usually associated with the Devil. It can also be called a Hellhound or Black Shuck (to name a few) and is often described as having glowing eyes, and a body much larger than a normal dog. In European mythology black dogs have often been connected with Death, and the underworld. When one is sighted it is said to be an omen of death, or at least a warning about an accident about to happen.
In recent years the black dog has come to be a symbol of depression, and so it could be a metephor for Elizabeth where, she goes searching for the black dog because she believes she saw it before her daughters untimely death. Then it can be left open to whether she just filled her life with this because of her loss or whether she genuinely saw the omen.
I am surprised I did not think of the black dog before, as the Grim in Harry Potter is based off of this legend. The script goes,
Seamus Finnigan: “The Grin? what’s the Grin?”
Bem: “Not the Grin, you idiot. The Grim. Taking the form of a giant spectral dog, it’s among the darkest omens in our world. It’s an omen…of death.”
(After Harry looks into his tealeaves)
An issue I thought about with doing this is that it won’t make for exciting images, as I have only thought of taking a shot of a large paw print on the ground, and finding chunks of fur. It’s not quite the exciting search I was planning on for Elizabeth.