Ms Graham, 25, grew up in Mt Wellington but now lives in Manurewa, South Auckland.
She was not due to give birth until January 11 and had planned a quiet New Year's Eve in. "My waters broke at about 3pm and then we were just waiting. We came to the hospital at about six o'clock. I thought: 'Well, the baby's going to be born in 2015 or 2016. It's going to be one of those dates anyway," she laughed.
The young mother had decided not to find out her child's gender until the birth and was not too surprised that she had another girl.
"There are lots of females in my family. Lots of sisters. Her coming early was the only surprise - a good one, though," Ms Graham said.
Grandmother Lee-Anne Graham said the family had quickly gathered to be by her daughter's side and would be supporting her over the next few months.
Mrs Graham said the latest addition was their fifth grandchild, all of whom were girls.
The new baby is also a great-grand-daughter to the family's matriarch, Marion Rhiand.