Racer Kid Pony

I loved this book when I was a kid but now can't find my copy or remember what it was called. I've told my niece about it though and she really wants to read it!
Its about a girl who dreams of a horse- a "beautiful black stallion with flowing mane and tail" - so she saves up but only has a few dollars. She uses this to buy a scruffy lame black pony as she feels sorry for him. She fixes him up but can't ride him as he has a jolting uncomfortable trot. She discovers however that he does know how to pull a cart. she still feels ashamed of him though especially as a girl nearby with a chestnut mare (with a "very smooth trot") teases her for not being able to ride her "stupid pony". One day whilst she's out with him, a couple stop her in excitement. It turns out he used to belong to them but was stolen as he was a champion trotting racer pulling a sulky. They say she can keep him as his injury means he can't race but I think they use him for stud still
Many thanks, hope you can help!