I might be wrong but I don't think I'd bother worrying about "character studies for toddlers".
Last thing I knew toddlers are learning through their senses (sight, sound, smell, taste, touch), their environment ("I feel safe", "I feel safe enough to explore this world", or "something scares me"), and maybe more than any of us dare to admit, their relationships with the people and the living things around them. That's where they'll learn about character - hands-on, sensory, environmental, relational. And I think you'll see their young spirits respond to and imitate what they see and experience in the people who surround them day in and day out.
Something to explore: At what age would you start focusing on character? At what age do children differentiate between good, bad, and just different? What makes something good? What makes it bad? I don't think we talk about it. I think we take whatever those words mean for granted.
Children begin to imitate those around them at a very young age. Who and what they're encouraged to imitate will definitely impact their character. Use it to your advantage and the glory of God.