What you're wanting is Conditional Fields. Sorry, this is not available currently. We've plans to implement conditional fields into CB 2.0, but that is a ways off from now. Only conditional field I've heard of (don't have links) is a Country > State > City type field.
You could actually do what your wanting using CBSubs however as plans are capable of "hiding" fields on registration. So for example you could have 2 plans (Animal and Plant) the user selects Animal and the Plants field hides (and vise verse of course) where user could then choose their type (dog, cat, etc..).