In today's NASA briefing about Monday's solar eclipse, co-chair of the National Solar Eclipse Task Force Angela Speck remarked, "It’s no different than any other day. On a normal day your pets don’t try to look at the sun and therefore don’t damage their eyes, so on this day they’re not going to do it either." https://youtu.be/SI9AovFNVUQ?t=52m36s
Veterinarian Dr. Tom Reaping of Youngstown, Ohio says, "Pets have a built-in ability to not look at the sun anyways so they are not going to be looking at that area."
If you're still worried, simply keep your pets inside --with the shades drawn-- during the eclipse.
photo by Tom Shockey