autocomplete taxonomy field depend on another taxonomy field
I hope this is a drupal site on development state.

If it is possible to you, I recommend you to create just one taxonomy vocabulary, where Animal type are parent terms of Breeds terms as a tree:

Cat


Curl
Bengal


Dog


Afghan
Akita


Then you can use Simple Hierarchical Select or Hierarchical Select, where you can allow users to select a parent term first and then childs.

Hope this help, if you need help with views filters or things like that I can help you :)