A dog year is a unit of measurement equal to one seventh of a year, or approximately 52 days. It is primarily used to approximate the equivalent age of dogs and other animals with similar life spans. It is based upon a popular myth regarding the aging of dogs that states that a dog ages seven years in the time it takes a human to age one year.
Here "dog years' might refer to the fact that the speaker is younger, but the amount is only countable when it is expressed in 'dog years". In other words, the amount is less than a normal year.