Any color will fade over time when exposed to UV light. But my experience has been that a good high quality fabric will hold up better over time. So for this quilt I would use either Moda Bella solids black or Kaufman Kona in black. Either will work well.
I made a quilt with a predominantly black background for my brother. It was not a solid but a mottled dark done with fossil ferns line. He does not have pets and the quilt is not exposed to direct sunlight and it looks as good as the day I made it 5 years later. However, while hand quilting it, every cat hair showed up like crazy on it. I had 5 at the time and all are light in color. It took two washes and about half of one sticky tape roller to get it all off.
So if your GD has light colored cats or dogs allowed on furniture then, yes their fur will show up on that black like all get out. But I don't think that should deter you. It is a beautiful quilt and I love brights mixed with black. It is so striking and that is a gorgeous quilt you pictured.