That's exacty what it sounds like. Well maybe not - is it a scooter your dog rides around town? No. You ride it and he/she/they pull you. (Hey Cash! I think I see something you need!!)
This all started here in the States, with a move to Seattle and a Rottweiler named (wait for it) Rubromarginata, in 1995. The Europeans beat us to it, of course. But long story short, with at least $250 (tiny folding model) and a mutt, you could be scootering. Or perhaps riding a sulky, or a trailer.
Why dontcha go here and learn all about it?