From my experience to get the bunny pet:
1. Uninstall Terraria completely. Make sure your characters and worlds are saved to the cloud.
2. Plug in the collectors edition disk, and open the files for it.
3. Run Bunny.exe, once you run it, there should be a pop up that says something like, "The bunny pet has been activated"
4. From here you can exit everything and even remove the disk from the computer entirely.
5. Re-install Terraria from the steam library, wait about 5-10 minutes for it to install, and open the game
6. Now all you have to do is to make a new character, enter a world, and you should have the bunny pet!
(7). If you don't have the bunny pet, uninstall Terraria again, and plug the disk back into the computer. Re-run the bunny.exe pet, and keep the disk plugged in. Now, with the disk plugged in, install Terraria from the steam library. Now, once it's done installing, you can remove the disk. If you did this correctly, you should be able to play Terraria with the bunny pet just like I mentioned in step 6.
Reminder to not install Terraria from the disk itself, for me it didn't even finish installing after 20 minutes, when installing Terraria normally took me 5 minutes. If it works for you, go ahead.