If you remember the dialog, the movie actually mentions Admiral Archer's beagle.Yes, and Memory Alpha pointed out that Archer would've been 145 at the time of Abrams-Trek, which I personally think it more than pushing it.
Archer himself could have been dead a half century by that point.
My private theory is that Porthos is also dead by that time, but his body is preserved and on display at Starfleet Academy, Porthos is Starfleet's mascot. Scotty stole it from the student union for his transporter experiment.
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Recent issue of the comic showed a living dog in the experiment. It's also made clear that Archer is alive.
Although they don't actually go the full distance and confirms that it is Jonathan Archer. In fact, given that Admiral Archer is apparentally still on active duty, it kind of implies it's not him.