If you log into Roblox: Grow A Garden after the event is already live, you won't receive the Chicken Zombie. As such, the only way to currently get this pet is by trading.

If you're looking for some multiplayer zombie action, then Roblox Zombie Attack should be your next stop.

Roblox Grow A Garden has many things you can do, including apparently getting a chicken...who is also a zombie. Go figure.