When you're saying "Které je to ditě" you're saying "Which child is that?" When you're saying "které ditě to je?" you're saying "Which child is it?"

"Které je to dítě" was just accepted for me.

Sometimes Duolingo offers "correct" answers that seem strange. This usually happens when we type something that is not quite right, but is similar to another acceptable translation. Your answer, "Čí je to dítě," means, "Whose child is it," which is why it was not accepted. But since it's structurally close to "Jaké je to dítě," which is accepted, Duo chose that as the correction to show you.

That would be "what is that child like?", I believe.

Yes, it is incorrect. Děvče is "girl."

Both to je and je to are accepted.