I had 2 crocs previously on my warrior, and got a 3rd one by chance because I was in shat at the time. I then did the quest on my priest and mage and got the pet both times. Fortunately the quest appeared for the next two days. On both these chars I got the other two pets for both chars.
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According to Warcraftpets.com, there is speculation that the new drop rate is 50% or more for the pets, which is much more optimistic for collectors than the previous 2% or lower.