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This site uses the EDICT and KANJIDIC dictionary files. These files are the property of the Electronic Dictionary Research and Development Group, and are used in conformance with the Group's licence.
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).