I was thinking of an image of an aged, made-up Bakula holding a puddle of goo at the end of a leash.
Porthos will be a very old dog in 2245!!
On a serious note, I've never taken the "Admiral Archer's prized beagle" comment to mean Porthos. I would imagine Porthos is well dead by then, and Archer (like most dog owners that prefer a certain breed) simply has another beagle. Well, had, since Scotty zaps him with the transporter...