I've had the Blue Jay for 4 days now. I never have an option to change it.?

Click on the paw print (main screen bottom centre). That will bring you to all of your wildlife animals. Choose a new animal and click “swap”. Then click the round icon above it that will start feeding your animal. The length of feeding (or drinking or playing) varies. 30 min for the lowest/common ones to 2 hours for epic ones. The new animals after the latest update Tun for 8 hours, great for overnight.

When your animal is done feeding, you’ll see a banner that says “collect” click on it to collect rewards. You can feed the same animal over and over again until it goes to sleep. Then you click the animal paw at the bottom and switch to another animal.