Learn Croatian: Ovo dijete je doma. - This child is at home.

Ovo is the neuter form of the word for "this". It must match the noun it describes. Since dijete (child) ends in -e, it is a neuter noun, so we use the neuter pronoun ovo.

Could I put the verb je right after Ovo, like Ovo je dijete doma?

You could, but it changes the meaning. Ovo dijete belongs together as a single block meaning "this child". If you put je between them, it breaks the block and the sentence changes to mean "This is a child at home."

Why is the word for "at home" doma instead of just dom?

Dom is the noun meaning "home", but doma is a special adverb that means "at home". It describes location, so you do not need to add an extra preposition like "in" or "at" before it.

I have also learned kod kuće for "at home". Can I use that here?

Yes! Ovo dijete je kod kuće is completely correct and means the exact same thing. Doma is just a shorter, very common alternative used in everyday speech.