The Ponytail Palm is a plant that is safe for dogs. It’s also fun. Ponytail Palms have a thick trunk and long, thin leaves that sprout out of the top like a wild, voluminous hairstyle. On top of adding a fun plant to your home that won’t hurt your dog, these plants are often referred to as “plants of steel” because they are considered relatively indestructible and are known for being easy to take care of.