When you start talking about breeding, i also have a question

Here goes: Can i start breeding when i only have the tiny bronco, or do i got to have the highwind? I've read that you need a chocobo from the Icicle area, and i'm not sure whether i can get there without the airship. And when i go to the chocobo farm, i don't get any question about buying stalls. Do i need to go to the house at the farm? I only went to the stalls there.