I may have found the information you were looking for. see link:
http://search.ancestry.com/cgi-bin/sse.dll?db=nypl&gss=s... The first entry Anna Storm has some of the info that matches your profile, Anna died at sea per the ships manifest see last column. Line -19 the name is blank but the age is listed as 7. On lines 20 Willi age: 3 Male and Line 21 Attilie age: 11 mos Female both also died. Line 22 Hermine
age: 1mo. Female did survive along with Katherine which I believe would be Line -19. Manifest is damaged. Her husband apparently did not accompany the family.
Tim