The little girl was listed with a bunch of other people at "Charity Hospital."She was the only child listed on this page.
1850 United States Federal Census > Louisiana > Orleans > Representative District 3 > Page 356 Charity Hospital Catharina Sturla, 8, female, b Sardinia
I can't find her in the index for the 1860 census in any place in the US.It's possible she died (if she was very ill), or that she had already married.
Have you been able to find out when your family immigrated to the US?Their immigration papers should list the port at which they arrived and the approximate date.That would confirm the New Orleans birth for Lawrence.I would also be really surprised if Lawrence wasn't baptised soon after his birth -- most Italian families were Catholic.I'm not sure where to get the Diocese of New Orleans baptismal records, though -- the Family History Centers may be able to help you with that.