What do you call a person who studies crocodiles?

A herpetologist is a person who studies reptiles and amphibians (including turtles).

The specific term for someone who studies turtles is testudinologist. A more general term that includes terrapins and tortoises is cheloniologist. Both Words return many hundreds of hits on google.

You could also say the Queen of Hearts piqued Alice's interest in psuedotestudinology though you are unlikely to find many hits for the Word on google.