Nearly one-fourth of all children were still-born. Many died from trismus nascentium, a form of tetanus that often caused death within the first ten days or so. It is possible they were buried in unmarked graves or graves bearing merely the name "Infant," as is so often the case throughout the United States.
An excellent cemetery guide is New Orleans Guide: with Descriptions. It includes a list of half a dozen cemeteries, their history, and where concentrations of Creole and other groups might be found.
An odd sort of article in the Western Journal of Medicine and Surgery, author, Dr. Dowler, deduces the average age of those buried in various cemeteries. In so doing, he documents these cemeteries and their "residents."
Dowler also mentions that most interments in the Bayou Cemetery or Potter's Field have no inscriptions. Since many people died as soon as they arrived, their names on the ship passenger's list is probably one of the last records of their whereabouts.
A good source for researching epidemic burials is the "List of interments in the different cemeteries of New Orleans and city of Lafayette, during the epidemic of 1847." The International Jewish Cemetery Project has information online about Jewish cemeteries in New Orleans.
Given the cost of the trip, it is highly unlikely that a body would be returned to Europe for burial. It also appears rare that a body was disposed of at sea. Passenger lists bear notes of those who died at sea. The early ship passenger lists had little oversight or regulation, but captains appear to have been careful to note those who died.
Traditions on land varied. During some epidemics, burial was slowed because religious belief prevented grave-diggers from burying a body before the ground had been consecrated. As a result, bodies remained above-ground waiting for ritual to be carried out. Of course, this meant that dead bodies bearing the epidemic were left in open air, possibly contributing to the epidemic. Apparently the grave-diggers were more afraid of failing to honor religious belief than they were of spreading the epidemic or falling prey to it.
Death is prevalent in a city that has experienced so many epidemics. The graveyards in New Orleans are even referred to "necropolises."