I quite like "Dog Years" now, but I also suspect the song has tongue in cheek. "For every sad son of a bitch"? Would Peart have perpetrated such a pun if he weren't trying to be funny?
That said, I agree that the song isn't mere filler or fluff, silly as its lyrics may be. And I will defend the lines about preferring to be "a tortoise on Galapagos or a span of geological time"--they're definitely lyrics by Neil Peart, that's for sure, and just take a moment to try to imagine how one could conceivably be (rather than endure for) a span of geological time. A mindbender, that one!
I also really like the opening bars that chug along with heavy cymbal--as MiriyaB noted, it sounds very reminiscent of X (another outstanding band that's effectively a musical trio + singer, to borrow Geddy's characterization of the Who).