Yes it's normal! I got Muffy, my miniature schnauzer, when I was 3 years old. When I was 16 she was diagnosed with cancer and eventually had to be put down. I spent most of my life with that dog. People say I'm crazy for saying this, but she really was like a sister to me. I'm almost 19 now and I still miss her like crazy. It sometimes still brings tears to my eyes when I think about her. I love my new dog, Ruby, but she will never replace Muffy. But no dog could ever replace Ruby either.