There is a KITTY MOODY on the 1870 census in Essex County, although not exactly the way you listed them there are 2 childrn with the same names you listed:

KITTY MOODY, age 37, Female, Black, Domestic Servant
JULIA, age 6, female, black, at home
JACOB, AGE 4, male black, at home
JOHN, age 1, male, black, at home

Although listed as 42 in 1880 not unusual to have ages off by 4 or 5 years or more.

How old was JULIA and JACOB in 1880.

Selma