There aren't many known instances of Dipstick's personality as a pup in the animated or live-action movies, however the series gives him a whole new look and at least some indication of personality.
Whatever Mooch does or wants him to do and doesn't seem to mind; even being hung from a clothespin and shaken like a leaf as evidenced in the series episode Love Em and Flea Em. He is often seen laughing at Mooch's jokes at the cruel expense of someone else, and loves playing practical jokes on others. He also loves junk food, often aiding Mooch and Wizzer in stealing from the pantry in order to obtain it. However, he doesn't appear to like getting in trouble, as seen in the episode Twelve Angry Pups. When Spot quizzed him on who he'd been with and what he'd been doing, he broke down in noisy tears, most likely afraid he was going to get in big trouble. He also exhibits a gullible and naive streak as evidenced in Walk on the Wild Side, being unable to recognize Swamp Rat or Rolly in disguise when it was clearly obvious.