Einstein (often known as "Einie") was Doc Brown's pet sheepdog in 1985, and later pet to the Brown family. His age in 1985 was unknown, although he was fully grown and most likely "middle aged" for a dog. He was the latest of many Doc's pet dogs named after famous scientists, in this case Albert Einstein. It was, therefore, quite fitting that he became the world's first time traveler.
Einstein was Doc's constant companion, and despite being using the dog in many of his experiments, Doc did care about his pet deeply (since apart from Marty McFly and Jennifer, Einstein appears to have been Doc's only friend), and he would not compromise his friend's safety. Doc built an automatic dog food feeder to make both his and Einstein's lives easier. Einstein was also "friends" with Marty and was usually a cheerful, friendly dog. He only liked canned dog food, as Doc pointed out in his letter to Marty, and was usually walked twice a day. He also enjoys liver treats given to him by Doc.