The phrase "dog's age" is typically used to describe a long period of time, often implying that it has been a very long time since something happened. However, there are plenty of other words and phrases that can be used to convey a similar idea. For example, you might say that something hasn't happened in "ages", "forever", or "an eternity". Alternatively, you could describe something as having taken place "a lifetime ago", "in the distant past", or "at the beginning of time". Overall, there are many ways to express the idea of a long period of time, so don't feel like you have to rely on just one phrase.