Mudguard, I think you're on the right track !
English, German, Dutch and French all have -pig for "guinea pig" (Schweinchen, zwijn, cochon) plus either Meer- or Guinea or Indes, indicating where the animal came from... BUT, Spanish is different and calls it a "little rabbit from the Indes" - conejillo de Indias. "Conejillo" is a little rabbit or bunny - much more cuddly.
So guinea pig is a very likely contender for what the creature in the story might be. Clearly, when these creatures first arrived in Europe (I read that this was in the 1500s) nobody knew what to call them - I've always thought they are very *unlike* pigs.