I recall OKCupid could ban you if you didn't provide a picture.

Do they actually check to see if it's actually a person of you? Or could you provide, say, a picture of a fluffy bunny?

If it's flagged, actual people will review the primary profile picture and decide whether they believe it is a picture of the account holder that meets their (quite reasonable) guidelines. Jokes, nudity, too close, too far away, obvious fakes, etc. will get your account locked.

So no, a picture of your pet rabbit will NOT work as a primary profile picture.