Nabaztag and Karotz were internet connected "rabbits" They are quite old, and getting hard to find - but here is some information about them.

https://en.wikipedia.org/wiki/Nabaztag https://nabaztag.com/#

These can still be setup, using the above website, but are limited as to what they can do. These were originally a French project/company - and the English translation is sometimes a little funky.

http://nabaztag.wizz.cc/ http://www.openkarotz.org/ http://opennag.net/

There are a few projects that take the shells, and put a raspberry pi in them, I couldn't find any of these projects right now.