Short-legged canine (5)
(Other definitions for dachshund that I've seen before include "Long, low dog" , "Small dog (from Germany?)" , "Sausage dog" , "Dad's hunch about the dog" , "low-down dog" .)
(Other definitions for corgi that I've seen before include "Pre-2018 royal dog" , "Welsh breed of short-legged dog" , "Small Welsh dog with fox-like head" , "man's best friend" , "pet in 9 [CARDIFF]?" .)