Well as far as I remember, Scotty says he beamed 'Admiral Archer's prize beagle'. They don't mention porthos by name.
It is probable that Archer is alive due to advances in medicine in the future. It is probable that when Porthos eventually died he got a new dog :) , or again with the appropriate pills Porthos became the oldest beagle on the planet(before Scotty beamed him into oblivion :D )
It also could be that the Admiral Archer to whom Scotty was referring was a descendant of Jonathan Archer. Somebody disagreed with the idea of a Captain's Dog. Beagles are also known for being the most common breed in the practice of vivisection of dogs.
You also cannot rule out the time travel option, as it was a main part of the plot in this very movie.
According to Roberto Orci and/or Alex Kurtzman, the "Admiral Archer" to which Scotty refers is, in fact, the Jonathan Archer, who was, at the time, well over 100. I don't know about the dog, although I personally hold it is Porthos.
Maybe Archer got another beagle. - Mitchz95 14:31, April 9, 2012 (UTC)
It is deffinitlly not Porthos.Dogs these days live about 15 years and humans 70-80-90 in future they live about 100-130 so at maximum dogs would be able to live 30 years in future but i doubt that same amount of effort was put to extend dogs life-span as it was put to extend humans or vulcans.Soo...Porthos is dead and Admiral Archer will be soon.Answer: HE GOT ANOTHER DOG