"Dogs ages" can be used to describe a long period of time, but there are many synonyms that can be used to convey this same idea. For instance, the phrase "dog's years" can be used to indicate a lengthy time period, similar to the original phrase. It can be also expressed as "a very long time," "an extended period," or "ages upon ages." Other synonyms include "eternity," "forever," and "since the dawn of time." Depending on the context, some other possible synonyms for "dogs ages" could be "a decade," "an era," or "a generation." Whatever the synonym, it's clear that this phrase indicates a significant and profound amount of time.