Hello, since Cristina is 8 in the 1901 census, she was born around 1893. You should be able to find her in the civil birth registrations records. You can search here:
In fact, I found a Julia Christina Hallinan born in Cork in 1893. That could well be the person you're looking for.
Since census ages are often just estimates by the census taker, you should always search for a span of years, I searched for 1890 to 1895. You should also not ask to match exactly, unless you're getting too many results. You can get the actual birth certificate with the information from this search. The cost is €20.
Civil registration of births began in 1864, and certificates are available for most births after that date. The certificate will give the father's name and the mother's maiden name.