Multiple realities
(covers information from several alternate timelines)
For the ships named Beagle, please see HMS Beagle and the SS Beagle.
The Beagle was a breed of domesticated dog, most likely originating from England, on Earth.
During the 22nd century, Captain Jonathan Archer owned a Beagle named Porthos, which he took with him during his ten-year mission on Enterprise. (ENT: "Broken Bow", "These Are the Voyages...")
Other than Porthos, Doctor Phlox had not treated any other beagles, (once mistakenly calling Porthos a "bugle",) but was able to find medical information on similar chordata in his sub-mammalian database. (ENT: "A Night in Sickbay")
In the alternate reality, Montgomery Scott attempted to prove his theories about interplanetary transportation by beaming Admiral Archer's prize Beagle. The dog was never seen again. (Star Trek)
In the novelization of Star Trek and the IDW comic "The Truth About Tribbles, Part 2", the dog re-materializes on the Enterprise, slightly confused but (apparently) quite unharmed.