Hi,
I am not American, but my baby is. She does not have a passport now, can I travel with her from OH to Caifornia by plane without it?

Looks like the rules are for people over 18. TSA: ID Requirements for Airport Checkpoints

The document you could carry is a "birth certificate". I would call the airline.

When you are travelling from one US location to another you will not be asked to go through customs. You may be asked for identification. Since you are a foreign citizen I think carrying the baby's birth certificate along with your own passport would be a good idea.