Most people get the quest for car form at lvls 16-18 depending on how strict/ nice your parents are. The quest is like the pally mount or warlock mount quest in that you need to spend some money to get it, normally 2-5k, and you need to have a "key" item in your inventory to use it.
Everyones car form looks different too, or maybe just a different color, so I hope yours looks good.