Actually this is one of the few Hindi sentences which seems wrong without an article.
We would say - जूलिया की एक बच्ची/बेटी है।
There is however one situation where your sentence could work. If a child is playing and someone asks you whose child that is - you could say
(वह) जूलिया की बच्ची है। It's/that's Julia's child.
Can we omit 'ek' and just say 'Julia bacci hai"? Is it necessary to include 'ek"?
Yes, that's quite common in colloquial Hindi around me. "Ek" literally translates as "one", it's probably mainly being used here to clarify between singular & plural for learning purposes.
I am guessing that the answer to that is - Can we say "Julia is child" in English.