A YouTube video posted by Amelia Glynn shows Jenny a pug puppy pushing her pug dollies in a pram around Portland, Oregon. The pink pram and the pink umbrella are an amusing sight.
You can watch it here:-
It does not look as if the pug is tied to the pram, and it is probably something that it learnt to do on its own, maybe from watching its owner and then being rewarded when it started to push the pram. 🙂