STORY OF SEASONS: Friends of Mineral Town

Angora rabbits can be bought from the beginning of the game from PoPoultry, which is immediately on your right as you exit your farm into Mineral Town. The store is open 11AM-4PM except Sundays and festival days. Angora rabbits cost 3000G each, so buying 4 outright will total 12000G. To get this easily, you can save inside PoPoultry, buy 4 Angora rabbits, wait for the achievement to pop (it will pop in the shop menu after you buy them all), and then reload.