Not only is it “normal” for you to have deeply felt memories of your dog, Carrie, it is sign of a wonderfully rich inner life. As we age, it is appropriate to revisit previous stages of our lives. Since your dog's life span coincided with a very formative phase of your life, you are probably experiencing emotions that encompass more than just your feelings for her.
You might want to explore certain reflective activities like journaling or writing down your memories of your childhood. You are lucky to have access to them through your connection to your dog. Perhaps you have family or friends who can share their recollections of her with you.
Thank you for your email, Carrie. It helped to remind many of us at the ASPCA why our relationship with animals is so important.