Oh, god, I loved that movie! Cried like a baby, too! At the time it first came out in the theatres, not only did we have a white lab (whose name rhymed with "Marley"), but he was an older dog, and even though he was very healthy, the movie reminded us that "that day will come someday."
Sadly, we lost the ol' puppy last summer. I just watched the movie again on cable recently, with my granddaughter, and it was hard to watch.
You're absolutely right about reaching that "Hey, you know what? I'M GONNA BE OKAY!" moment.