Winslow is immortal.In The Great Parent Mystery, he was an adult when he found the baby CatDog. Not to mention that he managed to live 1,000 years just by bodybuilding in the Bad Future episode.
CatDog are\is a Time Lord.Once there was a Prydonian Gallifreyan named Canisfelishivolar, or "Canfell" for short. When Canfell turned 8, he looked into the Eye of Harmony, and got enrolled at the Academy. The day right after Canfell got enrolled at the academy, he found a TARDIS and entered it as a stoveaway. As Canfell was a quite curious Gallifreyan, he jacked up quite a few commands, and as the TARDIS was already piloted by a twelfth regeneration Time Lord named Mr. Sunshine (who had already an adventure planned), Sunshine's TARDIS crashed in the planet CatDog is set in. The TARDIS crashed so hard, Mr. Sunshine lost all of his "time-lordiness" and fused with his old and now unusable TARDIS, while regenerating\transforming into a non-human-looking form, which is what we see today. Canfell also regenerated into his second regeneration, who, due to all the mutation from the TARDIS crash and Canfell himself being a rookie, regenerated into a form looking like a cat and a dog stitched to each other... but uh, he was ginger! Since he looked like a "baby" or little more than it, he was adopted by a monkey and a frog. Canfell was renamed some name such as Mark or George or whatever, and when he was around 4 or 5 (12 or 13 if you count his first incarnation) he got separated by his adoptive parents by a violent storm, found by an orphanothrophy, renamed himself "CatDog" after the animals he looked like, and thought the Gallifrey things were just from a cartoon show he had seen in his infancy, and that he just imagined them as real. CatDog grew other 21 (at least) years in his second incarnation, living as a native cat stitched to a native dog.
Rancid Rabbit's niece Rancy is really his daughter.She was born out of wedlock; he just says she's his niece to cover up the fact (and to avoid giving himself a bad name).
CatDog are neither cat nor dog.Despite their name, CatDog are not two separate creatures. In fact they are both the same species but have mutations that go beyond being conjoined at the hip, affecting their facial features so that each head resembles a canine and feline (kind of like how hyenas belong to their own family despite looking like cats/dogs). The reason why they act like their species' stereotype is due to social expectations, and lack of knowledge of their true origins. Further evidence for this comes from Mr. Sunshine, who doesn't fit in any category of recognizable species (human head, green skin, pig-like tail, etc.) It's likely CatDog don't belong in any of those categories either, but their physical features make them similar enough to cats and dogs that both they and other people think they really are cat and dog.