Mortimer is a black long haired dachshund. Here is a clip from NBC Sports showing a long haired dachshund competing at the 2021 National Dog Show. This dog is colored a golden brown, not black like Mortimer.
Here is another clip of a long haired dachshund competing at the 2022 National Dog Show also from NBC Sports.
Mr. Burns, a long haired dachshund, won the Hound Group at the 2019 Westminister Kennel Club Dog Show.
Mortimer is a show dog in the story so this is what he would do when he was working.