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The bird counter (羽) is the "correct" counter according to dictionaries and textbooks, but the counter for small animals (匹) is more commonly used in everyday language for rabbits.
There is a detailed (Japanese) article on it that you can read here (https://www.anicom-sompo.co.jp/usagi/2670.html).
Apparently the counter for large animals (頭) is also commonly used for rabbits in pet shops (this applies for dogs and cats as well).